restricted divisors of the first 1000 positive integers


In the table below, the proper divisors (or restricted divisors) of the first thousand positive integers are listed in the right column. That is, given divisorsMathworldPlanetmathPlanetmath 1,d2,,dk-1,n, with k being the total number of divisors and dk=n, only d2 through dk-1 are listed in the table below.

n Divisors 1<d<n
1 None
2 None
3 None
4 2
5 None
6 2, 3
7 None
8 2, 4
9 3
10 2, 5
11 None
12 2, 3, 4, 6
13 None
14 2, 7
15 3, 5
16 2, 4, 8
17 None
18 2, 3, 6, 9
19 None
20 2, 4, 5, 10
21 3, 7
22 2, 11
23 None
24 2, 3, 4, 6, 8, 12
25 5
26 2, 13
27 3, 9
28 2, 4, 7, 14
29 None
30 2, 3, 5, 6, 10, 15
31 None
32 2, 4, 8, 16
33 3, 11
34 2, 17
35 5, 7
36 2, 3, 4, 6, 9, 12, 18
37 None
38 2, 19
39 3, 13
40 2, 4, 5, 8, 10, 20
41 None
42 2, 3, 6, 7, 14, 21
43 None
44 2, 4, 11, 22
45 3, 5, 9, 15
46 2, 23
47 None
48 2, 3, 4, 6, 8, 12, 16, 24
49 7
50 2, 5, 10, 25
51 3, 17
52 2, 4, 13, 26
53 None
54 2, 3, 6, 9, 18, 27
55 5, 11
56 2, 4, 7, 8, 14, 28
57 3, 19
58 2, 29
59 None
60 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
61 None
62 2, 31
63 3, 7, 9, 21
64 2, 4, 8, 16, 32
65 5, 13
66 2, 3, 6, 11, 22, 33
67 None
68 2, 4, 17, 34
69 3, 23
70 2, 5, 7, 10, 14, 35
71 None
72 2, 3, 4, 6, 8, 9, 12, 18, 24, 36
73 None
74 2, 37
75 3, 5, 15, 25
76 2, 4, 19, 38
77 7, 11
78 2, 3, 6, 13, 26, 39
79 None
80 2, 4, 5, 8, 10, 16, 20, 40
81 3, 9, 27
82 2, 41
83 None
84 2, 3, 4, 6, 7, 12, 14, 21, 28, 42
85 5, 17
86 2, 43
87 3, 29
88 2, 4, 8, 11, 22, 44
89 None
90 2, 3, 5, 6, 9, 10, 15, 18, 30, 45
91 7, 13
92 2, 4, 23, 46
93 3, 31
94 2, 47
95 5, 19
96 2, 3, 4, 6, 8, 12, 16, 24, 32, 48
97 None
98 2, 7, 14, 49
99 3, 9, 11, 33
100 2, 4, 5, 10, 20, 25, 50
101 None
102 2, 3, 6, 17, 34, 51
103 None
104 2, 4, 8, 13, 26, 52
105 3, 5, 7, 15, 21, 35
106 2, 53
107 None
108 2, 3, 4, 6, 9, 12, 18, 27, 36, 54
109 None
110 2, 5, 10, 11, 22, 55
111 3, 37
112 2, 4, 7, 8, 14, 16, 28, 56
113 None
114 2, 3, 6, 19, 38, 57
115 5, 23
116 2, 4, 29, 58
117 3, 9, 13, 39
118 2, 59
119 7, 17
120 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60
121 11
122 2, 61
123 3, 41
124 2, 4, 31, 62
125 5, 25
126 2, 3, 6, 7, 9, 14, 18, 21, 42, 63
127 None
128 2, 4, 8, 16, 32, 64
129 3, 43
130 2, 5, 10, 13, 26, 65
131 None
132 2, 3, 4, 6, 11, 12, 22, 33, 44, 66
133 7, 19
134 2, 67
135 3, 5, 9, 15, 27, 45
136 2, 4, 8, 17, 34, 68
137 None
138 2, 3, 6, 23, 46, 69
139 None
140 2, 4, 5, 7, 10, 14, 20, 28, 35, 70
141 3, 47
142 2, 71
143 11, 13
144 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72
145 5, 29
146 2, 73
147 3, 7, 21, 49
148 2, 4, 37, 74
149 None
150 2, 3, 5, 6, 10, 15, 25, 30, 50, 75
151 None
152 2, 4, 8, 19, 38, 76
153 3, 9, 17, 51
154 2, 7, 11, 14, 22, 77
155 5, 31
156 2, 3, 4, 6, 12, 13, 26, 39, 52, 78
157 None
158 2, 79
159 3, 53
160 2, 4, 5, 8, 10, 16, 20, 32, 40, 80
161 7, 23
162 2, 3, 6, 9, 18, 27, 54, 81
163 None
164 2, 4, 41, 82
165 3, 5, 11, 15, 33, 55
166 2, 83
167 None
168 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84
169 13
170 2, 5, 10, 17, 34, 85
171 3, 9, 19, 57
172 2, 4, 43, 86
173 None
174 2, 3, 6, 29, 58, 87
175 5, 7, 25, 35
176 2, 4, 8, 11, 16, 22, 44, 88
177 3, 59
178 2, 89
179 None
180 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90
181 None
182 2, 7, 13, 14, 26, 91
183 3, 61
184 2, 4, 8, 23, 46, 92
185 5, 37
186 2, 3, 6, 31, 62, 93
187 11, 17
188 2, 4, 47, 94
189 3, 7, 9, 21, 27, 63
190 2, 5, 10, 19, 38, 95
191 None
192 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96
193 None
194 2, 97
195 3, 5, 13, 15, 39, 65
196 2, 4, 7, 14, 28, 49, 98
197 None
198 2, 3, 6, 9, 11, 18, 22, 33, 66, 99
199 None
200 2, 4, 5, 8, 10, 20, 25, 40, 50, 100
201 3, 67
202 2, 101
203 7, 29
204 2, 3, 4, 6, 12, 17, 34, 51, 68, 102
205 5, 41
206 2, 103
207 3, 9, 23, 69
208 2, 4, 8, 13, 16, 26, 52, 104
209 11, 19
210 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105
211 None
212 2, 4, 53, 106
213 3, 71
214 2, 107
215 5, 43
216 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108
217 7, 31
218 2, 109
219 3, 73
220 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
221 13, 17
222 2, 3, 6, 37, 74, 111
223 None
224 2, 4, 7, 8, 14, 16, 28, 32, 56, 112
225 3, 5, 9, 15, 25, 45, 75
226 2, 113
227 None
228 2, 3, 4, 6, 12, 19, 38, 57, 76, 114
229 None
230 2, 5, 10, 23, 46, 115
231 3, 7, 11, 21, 33, 77
232 2, 4, 8, 29, 58, 116
233 None
234 2, 3, 6, 9, 13, 18, 26, 39, 78, 117
235 5, 47
236 2, 4, 59, 118
237 3, 79
238 2, 7, 14, 17, 34, 119
239 None
240 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120
241 None
242 2, 11, 22, 121
243 3, 9, 27, 81
244 2, 4, 61, 122
245 5, 7, 35, 49
246 2, 3, 6, 41, 82, 123
247 13, 19
248 2, 4, 8, 31, 62, 124
249 3, 83
250 2, 5, 10, 25, 50, 125
251 None
252 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126
253 11, 23
254 2, 127
255 3, 5, 15, 17, 51, 85
256 2, 4, 8, 16, 32, 64, 128
257 None
258 2, 3, 6, 43, 86, 129
259 7, 37
260 2, 4, 5, 10, 13, 20, 26, 52, 65, 130
261 3, 9, 29, 87
262 2, 131
263 None
264 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132
265 5, 53
266 2, 7, 14, 19, 38, 133
267 3, 89
268 2, 4, 67, 134
269 None
270 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135
271 None
272 2, 4, 8, 16, 17, 34, 68, 136
273 3, 7, 13, 21, 39, 91
274 2, 137
275 5, 11, 25, 55
276 2, 3, 4, 6, 12, 23, 46, 69, 92, 138
277 None
278 2, 139
279 3, 9, 31, 93
280 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140
281 None
282 2, 3, 6, 47, 94, 141
283 None
284 2, 4, 71, 142
285 3, 5, 15, 19, 57, 95
286 2, 11, 13, 22, 26, 143
287 7, 41
288 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144
289 17
290 2, 5, 10, 29, 58, 145
291 3, 97
292 2, 4, 73, 146
293 None
294 2, 3, 6, 7, 14, 21, 42, 49, 98, 147
295 5, 59
296 2, 4, 8, 37, 74, 148
297 3, 9, 11, 27, 33, 99
298 2, 149
299 13, 23
300 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150
301 7, 43
302 2, 151
303 3, 101
304 2, 4, 8, 16, 19, 38, 76, 152
305 5, 61
306 2, 3, 6, 9, 17, 18, 34, 51, 102, 153
307 None
308 2, 4, 7, 11, 14, 22, 28, 44, 77, 154
309 3, 103
310 2, 5, 10, 31, 62, 155
311 None
312 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156
313 None
314 2, 157
315 3, 5, 7, 9, 15, 21, 35, 45, 63, 105
316 2, 4, 79, 158
317 None
318 2, 3, 6, 53, 106, 159
319 11, 29
320 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160
321 3, 107
322 2, 7, 14, 23, 46, 161
323 17, 19
324 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162
325 5, 13, 25, 65
326 2, 163
327 3, 109
328 2, 4, 8, 41, 82, 164
329 7, 47
330 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165
331 None
332 2, 4, 83, 166
333 3, 9, 37, 111
334 2, 167
335 5, 67
336 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168
337 None
338 2, 13, 26, 169
339 3, 113
340 2, 4, 5, 10, 17, 20, 34, 68, 85, 170
341 11, 31
342 2, 3, 6, 9, 18, 19, 38, 57, 114, 171
343 7, 49
344 2, 4, 8, 43, 86, 172
345 3, 5, 15, 23, 69, 115
346 2, 173
347 None
348 2, 3, 4, 6, 12, 29, 58, 87, 116, 174
349 None
350 2, 5, 7, 10, 14, 25, 35, 50, 70, 175
351 3, 9, 13, 27, 39, 117
352 2, 4, 8, 11, 16, 22, 32, 44, 88, 176
353 None
354 2, 3, 6, 59, 118, 177
355 5, 71
356 2, 4, 89, 178
357 3, 7, 17, 21, 51, 119
358 2, 179
359 None
360 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
361 19
362 2, 181
363 3, 11, 33, 121
364 2, 4, 7, 13, 14, 26, 28, 52, 91, 182
365 5, 73
366 2, 3, 6, 61, 122, 183
367 None
368 2, 4, 8, 16, 23, 46, 92, 184
369 3, 9, 41, 123
370 2, 5, 10, 37, 74, 185
371 7, 53
372 2, 3, 4, 6, 12, 31, 62, 93, 124, 186
373 None
374 2, 11, 17, 22, 34, 187
375 3, 5, 15, 25, 75, 125
376 2, 4, 8, 47, 94, 188
377 13, 29
378 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189
379 None
380 2, 4, 5, 10, 19, 20, 38, 76, 95, 190
381 3, 127
382 2, 191
383 None
384 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192
385 5, 7, 11, 35, 55, 77
386 2, 193
387 3, 9, 43, 129
388 2, 4, 97, 194
389 None
390 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195
391 17, 23
392 2, 4, 7, 8, 14, 28, 49, 56, 98, 196
393 3, 131
394 2, 197
395 5, 79
396 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198
397 None
398 2, 199
399 3, 7, 19, 21, 57, 133
400 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200
401 None
402 2, 3, 6, 67, 134, 201
403 13, 31
404 2, 4, 101, 202
405 3, 5, 9, 15, 27, 45, 81, 135
406 2, 7, 14, 29, 58, 203
407 11, 37
408 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204
409 None
410 2, 5, 10, 41, 82, 205
411 3, 137
412 2, 4, 103, 206
413 7, 59
414 2, 3, 6, 9, 18, 23, 46, 69, 138, 207
415 5, 83
416 2, 4, 8, 13, 16, 26, 32, 52, 104, 208
417 3, 139
418 2, 11, 19, 22, 38, 209
419 None
420 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210
421 None
422 2, 211
423 3, 9, 47, 141
424 2, 4, 8, 53, 106, 212
425 5, 17, 25, 85
426 2, 3, 6, 71, 142, 213
427 7, 61
428 2, 4, 107, 214
429 3, 11, 13, 33, 39, 143
430 2, 5, 10, 43, 86, 215
431 None
432 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216
433 None
434 2, 7, 14, 31, 62, 217
435 3, 5, 15, 29, 87, 145
436 2, 4, 109, 218
437 19, 23
438 2, 3, 6, 73, 146, 219
439 None
440 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220
441 3, 7, 9, 21, 49, 63, 147
442 2, 13, 17, 26, 34, 221
443 None
444 2, 3, 4, 6, 12, 37, 74, 111, 148, 222
445 5, 89
446 2, 223
447 3, 149
448 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224
449 None
450 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225
451 11, 41
452 2, 4, 113, 226
453 3, 151
454 2, 227
455 5, 7, 13, 35, 65, 91
456 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228
457 None
458 2, 229
459 3, 9, 17, 27, 51, 153
460 2, 4, 5, 10, 20, 23, 46, 92, 115, 230
461 None
462 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231
463 None
464 2, 4, 8, 16, 29, 58, 116, 232
465 3, 5, 15, 31, 93, 155
466 2, 233
467 None
468 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234
469 7, 67
470 2, 5, 10, 47, 94, 235
471 3, 157
472 2, 4, 8, 59, 118, 236
473 11, 43
474 2, 3, 6, 79, 158, 237
475 5, 19, 25, 95
476 2, 4, 7, 14, 17, 28, 34, 68, 119, 238
477 3, 9, 53, 159
478 2, 239
479 None
480 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240
481 13, 37
482 2, 241
483 3, 7, 21, 23, 69, 161
484 2, 4, 11, 22, 44, 121, 242
485 5, 97
486 2, 3, 6, 9, 18, 27, 54, 81, 162, 243
487 None
488 2, 4, 8, 61, 122, 244
489 3, 163
490 2, 5, 7, 10, 14, 35, 49, 70, 98, 245
491 None
492 2, 3, 4, 6, 12, 41, 82, 123, 164, 246
493 17, 29
494 2, 13, 19, 26, 38, 247
495 3, 5, 9, 11, 15, 33, 45, 55, 99, 165
496 2, 4, 8, 16, 31, 62, 124, 248
497 7, 71
498 2, 3, 6, 83, 166, 249
499 None
500 2, 4, 5, 10, 20, 25, 50, 100, 125, 250
501 3, 167
502 2, 251
503 None
504 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252
505 5, 101
506 2, 11, 22, 23, 46, 253
507 3, 13, 39, 169
508 2, 4, 127, 254
509 None
510 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255
511 7, 73
512 2, 4, 8, 16, 32, 64, 128, 256
513 3, 9, 19, 27, 57, 171
514 2, 257
515 5, 103
516 2, 3, 4, 6, 12, 43, 86, 129, 172, 258
517 11, 47
518 2, 7, 14, 37, 74, 259
519 3, 173
520 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260
521 None
522 2, 3, 6, 9, 18, 29, 58, 87, 174, 261
523 None
524 2, 4, 131, 262
525 3, 5, 7, 15, 21, 25, 35, 75, 105, 175
526 2, 263
527 17, 31
528 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264
529 23
530 2, 5, 10, 53, 106, 265
531 3, 9, 59, 177
532 2, 4, 7, 14, 19, 28, 38, 76, 133, 266
533 13, 41
534 2, 3, 6, 89, 178, 267
535 5, 107
536 2, 4, 8, 67, 134, 268
537 3, 179
538 2, 269
539 7, 11, 49, 77
540 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270
541 None
542 2, 271
543 3, 181
544 2, 4, 8, 16, 17, 32, 34, 68, 136, 272
545 5, 109
546 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273
547 None
548 2, 4, 137, 274
549 3, 9, 61, 183
550 2, 5, 10, 11, 22, 25, 50, 55, 110, 275
551 19, 29
552 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 138, 184, 276
553 7, 79
554 2, 277
555 3, 5, 15, 37, 111, 185
556 2, 4, 139, 278
557 None
558 2, 3, 6, 9, 18, 31, 62, 93, 186, 279
559 13, 43
560 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280
561 3, 11, 17, 33, 51, 187
562 2, 281
563 None
564 2, 3, 4, 6, 12, 47, 94, 141, 188, 282
565 5, 113
566 2, 283
567 3, 7, 9, 21, 27, 63, 81, 189
568 2, 4, 8, 71, 142, 284
569 None
570 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285
571 None
572 2, 4, 11, 13, 22, 26, 44, 52, 143, 286
573 3, 191
574 2, 7, 14, 41, 82, 287
575 5, 23, 25, 115
576 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288
577 None
578 2, 17, 34, 289
579 3, 193
580 2, 4, 5, 10, 20, 29, 58, 116, 145, 290
581 7, 83
582 2, 3, 6, 97, 194, 291
583 11, 53
584 2, 4, 8, 73, 146, 292
585 3, 5, 9, 13, 15, 39, 45, 65, 117, 195
586 2, 293
587 None
588 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294
589 19, 31
590 2, 5, 10, 59, 118, 295
591 3, 197
592 2, 4, 8, 16, 37, 74, 148, 296
593 None
594 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 198, 297
595 5, 7, 17, 35, 85, 119
596 2, 4, 149, 298
597 3, 199
598 2, 13, 23, 26, 46, 299
599 None
600 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300
601 None
602 2, 7, 14, 43, 86, 301
603 3, 9, 67, 201
604 2, 4, 151, 302
605 5, 11, 55, 121
606 2, 3, 6, 101, 202, 303
607 None
608 2, 4, 8, 16, 19, 32, 38, 76, 152, 304
609 3, 7, 21, 29, 87, 203
610 2, 5, 10, 61, 122, 305
611 13, 47
612 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306
613 None
614 2, 307
615 3, 5, 15, 41, 123, 205
616 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308
617 None
618 2, 3, 6, 103, 206, 309
619 None
620 2, 4, 5, 10, 20, 31, 62, 124, 155, 310
621 3, 9, 23, 27, 69, 207
622 2, 311
623 7, 89
624 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312
625 5, 25, 125
626 2, 313
627 3, 11, 19, 33, 57, 209
628 2, 4, 157, 314
629 17, 37
630 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315
631 None
632 2, 4, 8, 79, 158, 316
633 3, 211
634 2, 317
635 5, 127
636 2, 3, 4, 6, 12, 53, 106, 159, 212, 318
637 7, 13, 49, 91
638 2, 11, 22, 29, 58, 319
639 3, 9, 71, 213
640 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320
641 None
642 2, 3, 6, 107, 214, 321
643 None
644 2, 4, 7, 14, 23, 28, 46, 92, 161, 322
645 3, 5, 15, 43, 129, 215
646 2, 17, 19, 34, 38, 323
647 None
648 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324
649 11, 59
650 2, 5, 10, 13, 25, 26, 50, 65, 130, 325
651 3, 7, 21, 31, 93, 217
652 2, 4, 163, 326
653 None
654 2, 3, 6, 109, 218, 327
655 5, 131
656 2, 4, 8, 16, 41, 82, 164, 328
657 3, 9, 73, 219
658 2, 7, 14, 47, 94, 329
659 None
660 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330
661 None
662 2, 331
663 3, 13, 17, 39, 51, 221
664 2, 4, 8, 83, 166, 332
665 5, 7, 19, 35, 95, 133
666 2, 3, 6, 9, 18, 37, 74, 111, 222, 333
667 23, 29
668 2, 4, 167, 334
669 3, 223
670 2, 5, 10, 67, 134, 335
671 11, 61
672 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336
673 None
674 2, 337
675 3, 5, 9, 15, 25, 27, 45, 75, 135, 225
676 2, 4, 13, 26, 52, 169, 338
677 None
678 2, 3, 6, 113, 226, 339
679 7, 97
680 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340
681 3, 227
682 2, 11, 22, 31, 62, 341
683 None
684 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342
685 5, 137
686 2, 7, 14, 49, 98, 343
687 3, 229
688 2, 4, 8, 16, 43, 86, 172, 344
689 13, 53
690 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345
691 None
692 2, 4, 173, 346
693 3, 7, 9, 11, 21, 33, 63, 77, 99, 231
694 2, 347
695 5, 139
696 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348
697 17, 41
698 2, 349
699 3, 233
700 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350
701 None
702 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351
703 19, 37
704 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352
705 3, 5, 15, 47, 141, 235
706 2, 353
707 7, 101
708 2, 3, 4, 6, 12, 59, 118, 177, 236, 354
709 None
710 2, 5, 10, 71, 142, 355
711 3, 9, 79, 237
712 2, 4, 8, 89, 178, 356
713 23, 31
714 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357
715 5, 11, 13, 55, 65, 143
716 2, 4, 179, 358
717 3, 239
718 2, 359
719 None
720 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360
721 7, 103
722 2, 19, 38, 361
723 3, 241
724 2, 4, 181, 362
725 5, 25, 29, 145
726 2, 3, 6, 11, 22, 33, 66, 121, 242, 363
727 None
728 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364
729 3, 9, 27, 81, 243
730 2, 5, 10, 73, 146, 365
731 17, 43
732 2, 3, 4, 6, 12, 61, 122, 183, 244, 366
733 None
734 2, 367
735 3, 5, 7, 15, 21, 35, 49, 105, 147, 245
736 2, 4, 8, 16, 23, 32, 46, 92, 184, 368
737 11, 67
738 2, 3, 6, 9, 18, 41, 82, 123, 246, 369
739 None
740 2, 4, 5, 10, 20, 37, 74, 148, 185, 370
741 3, 13, 19, 39, 57, 247
742 2, 7, 14, 53, 106, 371
743 None
744 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372
745 5, 149
746 2, 373
747 3, 9, 83, 249
748 2, 4, 11, 17, 22, 34, 44, 68, 187, 374
749 7, 107
750 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375
751 None
752 2, 4, 8, 16, 47, 94, 188, 376
753 3, 251
754 2, 13, 26, 29, 58, 377
755 5, 151
756 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378
757 None
758 2, 379
759 3, 11, 23, 33, 69, 253
760 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380
761 None
762 2, 3, 6, 127, 254, 381
763 7, 109
764 2, 4, 191, 382
765 3, 5, 9, 15, 17, 45, 51, 85, 153, 255
766 2, 383
767 13, 59
768 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384
769 None
770 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385
771 3, 257
772 2, 4, 193, 386
773 None
774 2, 3, 6, 9, 18, 43, 86, 129, 258, 387
775 5, 25, 31, 155
776 2, 4, 8, 97, 194, 388
777 3, 7, 21, 37, 111, 259
778 2, 389
779 19, 41
780 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390
781 11, 71
782 2, 17, 23, 34, 46, 391
783 3, 9, 27, 29, 87, 261
784 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392
785 5, 157
786 2, 3, 6, 131, 262, 393
787 None
788 2, 4, 197, 394
789 3, 263
790 2, 5, 10, 79, 158, 395
791 7, 113
792 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396
793 13, 61
794 2, 397
795 3, 5, 15, 53, 159, 265
796 2, 4, 199, 398
797 None
798 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399
799 17, 47
800 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400
801 3, 9, 89, 267
802 2, 401
803 11, 73
804 2, 3, 4, 6, 12, 67, 134, 201, 268, 402
805 5, 7, 23, 35, 115, 161
806 2, 13, 26, 31, 62, 403
807 3, 269
808 2, 4, 8, 101, 202, 404
809 None
810 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405
811 None
812 2, 4, 7, 14, 28, 29, 58, 116, 203, 406
813 3, 271
814 2, 11, 22, 37, 74, 407
815 5, 163
816 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408
817 19, 43
818 2, 409
819 3, 7, 9, 13, 21, 39, 63, 91, 117, 273
820 2, 4, 5, 10, 20, 41, 82, 164, 205, 410
821 None
822 2, 3, 6, 137, 274, 411
823 None
824 2, 4, 8, 103, 206, 412
825 3, 5, 11, 15, 25, 33, 55, 75, 165, 275
826 2, 7, 14, 59, 118, 413
827 None
828 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414
829 None
830 2, 5, 10, 83, 166, 415
831 3, 277
832 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416
833 7, 17, 49, 119
834 2, 3, 6, 139, 278, 417
835 5, 167
836 2, 4, 11, 19, 22, 38, 44, 76, 209, 418
837 3, 9, 27, 31, 93, 279
838 2, 419
839 None
840 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420
841 29
842 2, 421
843 3, 281
844 2, 4, 211, 422
845 5, 13, 65, 169
846 2, 3, 6, 9, 18, 47, 94, 141, 282, 423
847 7, 11, 77, 121
848 2, 4, 8, 16, 53, 106, 212, 424
849 3, 283
850 2, 5, 10, 17, 25, 34, 50, 85, 170, 425
851 23, 37
852 2, 3, 4, 6, 12, 71, 142, 213, 284, 426
853 None
854 2, 7, 14, 61, 122, 427
855 3, 5, 9, 15, 19, 45, 57, 95, 171, 285
856 2, 4, 8, 107, 214, 428
857 None
858 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429
859 None
860 2, 4, 5, 10, 20, 43, 86, 172, 215, 430
861 3, 7, 21, 41, 123, 287
862 2, 431
863 None
864 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432
865 5, 173
866 2, 433
867 3, 17, 51, 289
868 2, 4, 7, 14, 28, 31, 62, 124, 217, 434
869 11, 79
870 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435
871 13, 67
872 2, 4, 8, 109, 218, 436
873 3, 9, 97, 291
874 2, 19, 23, 38, 46, 437
875 5, 7, 25, 35, 125, 175
876 2, 3, 4, 6, 12, 73, 146, 219, 292, 438
877 None
878 2, 439
879 3, 293
880 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440
881 None
882 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441
883 None
884 2, 4, 13, 17, 26, 34, 52, 68, 221, 442
885 3, 5, 15, 59, 177, 295
886 2, 443
887 None
888 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444
889 7, 127
890 2, 5, 10, 89, 178, 445
891 3, 9, 11, 27, 33, 81, 99, 297
892 2, 4, 223, 446
893 19, 47
894 2, 3, 6, 149, 298, 447
895 5, 179
896 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448
897 3, 13, 23, 39, 69, 299
898 2, 449
899 29, 31
900 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450
901 17, 53
902 2, 11, 22, 41, 82, 451
903 3, 7, 21, 43, 129, 301
904 2, 4, 8, 113, 226, 452
905 5, 181
906 2, 3, 6, 151, 302, 453
907 None
908 2, 4, 227, 454
909 3, 9, 101, 303
910 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455
911 None
912 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456
913 11, 83
914 2, 457
915 3, 5, 15, 61, 183, 305
916 2, 4, 229, 458
917 7, 131
918 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459
919 None
920 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460
921 3, 307
922 2, 461
923 13, 71
924 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462
925 5, 25, 37, 185
926 2, 463
927 3, 9, 103, 309
928 2, 4, 8, 16, 29, 32, 58, 116, 232, 464
929 None
930 2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465
931 7, 19, 49, 133
932 2, 4, 233, 466
933 3, 311
934 2, 467
935 5, 11, 17, 55, 85, 187
936 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468
937 None
938 2, 7, 14, 67, 134, 469
939 3, 313
940 2, 4, 5, 10, 20, 47, 94, 188, 235, 470
941 None
942 2, 3, 6, 157, 314, 471
943 23, 41
944 2, 4, 8, 16, 59, 118, 236, 472
945 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315
946 2, 11, 22, 43, 86, 473
947 None
948 2, 3, 4, 6, 12, 79, 158, 237, 316, 474
949 13, 73
950 2, 5, 10, 19, 25, 38, 50, 95, 190, 475
951 3, 317
952 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476
953 None
954 2, 3, 6, 9, 18, 53, 106, 159, 318, 477
955 5, 191
956 2, 4, 239, 478
957 3, 11, 29, 33, 87, 319
958 2, 479
959 7, 137
960 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480
961 31
962 2, 13, 26, 37, 74, 481
963 3, 9, 107, 321
964 2, 4, 241, 482
965 5, 193
966 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483
967 None
968 2, 4, 8, 11, 22, 44, 88, 121, 242, 484
969 3, 17, 19, 51, 57, 323
970 2, 5, 10, 97, 194, 485
971 None
972 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486
973 7, 139
974 2, 487
975 3, 5, 13, 15, 25, 39, 65, 75, 195, 325
976 2, 4, 8, 16, 61, 122, 244, 488
977 None
978 2, 3, 6, 163, 326, 489
979 11, 89
980 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490
981 3, 9, 109, 327
982 2, 491
983 None
984 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492
985 5, 197
986 2, 17, 29, 34, 58, 493
987 3, 7, 21, 47, 141, 329
988 2, 4, 13, 19, 26, 38, 52, 76, 247, 494
989 23, 43
990 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495
991 None
992 2, 4, 8, 16, 31, 32, 62, 124, 248, 496
993 3, 331
994 2, 7, 14, 71, 142, 497
995 5, 199
996 2, 3, 4, 6, 12, 83, 166, 249, 332, 498
997 None
998 2, 499
999 3, 9, 27, 37, 111, 333
1000 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500
Title restricted divisors of the first 1000 positive integers
Canonical name RestrictedDivisorsOfTheFirst1000PositiveIntegers
Date of creation 2013-03-22 16:52:42
Last modified on 2013-03-22 16:52:42
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Example
Classification msc 11A51