Find the smallest integer n such that both n-1 and n+1 have the same number of divisors as n.
Bonus task: List few additional numbers with said feature.

(In reply to re: computer solution by Jer)

Quints under 100,000:

  low      high  # of divisors
 11605 11609 8
 12855 12859 8
 13782 13786 8
 19142 19146 8
 21494 21498 8
 28374 28378 8 |
 28375 28379 8 | these make a hex
 40311 40315 8
 42805 42809 8
 50582 50586 8
 55254 55258 8
 60231 60235 8
 60663 60667 8
 79094 79098 8
 87655 87659 8
 90181 90185 8 |
 90182 90186 8 |  hex
 95845 95849 8
 99655 99659 8

and quads that are not in quints:

  range    # of divisors
 242 245 6
 3655 3658 8
 4503 4506 8
 5943 5946 8
 6853 6856 8
 7256 7259 8
 8392 8395 8
 9367 9370 8
 10983 10986 8
 12565 12568 8
 12872 12875 8
 13255 13258 8
 14312 14315 8
 16133 16136 8
 17095 17098 8
 18469 18472 8
 19045 19048 8
 19940 19943 12
 20165 20168 8
 20965 20968 8
 21368 21371 8
 21512 21515 8
 22855 22858 8
 23989 23992 8
 26885 26888 8
 28135 28138 8
 29605 29608 8
 30583 30586 8
 31735 31738 8
 31910 31913 8
 32005 32008 8
 32792 32795 8
 33062 33065 8
 33608 33611 8
 33845 33848 8
 34069 34072 8
 36392 36395 8
 37256 37259 8
 41335 41338 8
 43304 43307 8
 43526 43529 8
 43766 43769 8
 44213 44216 8
 45686 45689 8
 45733 45736 8
 47845 47848 8
 48054 48057 8
 49147 49150 12
 49765 49768 8
 51752 51755 8
 54103 54106 8
 54585 54588 12
 54966 54969 8
 55063 55066 8
 55976 55979 8
 56343 56346 8
 58952 58955 8
 59815 59818 8
 61142 61145 8
 62343 62346 8
 65334 65337 8
 66952 66955 8
 67015 67018 8
 68104 68107 8
 69303 69306 8
 71095 71098 8
 73927 73930 8
 74053 74056 8
 76262 76265 8
 76982 76985 8
 77432 77435 8
 78535 78538 8
 78872 78875 8
 79591 79594 8
 80726 80729 8
 82855 82858 8
 84469 84472 8
 86887 86890 8
 87896 87899 8
 91495 91498 8
 93063 93066 8
 94262 94265 8
 94645 94648 8
 95384 95387 8
 95414 95417 8
 95512 95515 8
 97255 97258 8
 98102 98105 8
 98984 98987 8

Posted by Charlie on 2014-04-18 22:14:13