cp's OEIS Frontend

A108825 Numbers j such that j divides the sum of the digits of j!.

%I A108825 #29 Feb 24 2024 01:11:39
%S A108825 1,2,3,9,15,18,21,27,72,81,234,462,502,522,1314,1323,3789,3897,6462,
%T A108825 10470,17532,17820,28503,48248,48254,48303,48644,48856,223551,226149,
%U A108825 227406,625986,4838918,4848004
%N A108825 Numbers j such that j divides the sum of the digits of j!.
%C A108825 Especially for larger values, terms can be expected to occur near values of k such that 4.5 times the number of digits in k!, not counting the digits in the string of trailing zeros, is approximately an integer multiple (m) of k. As m increases, such values of k approach k = e * 100^(m/9 + 1/8). - _Jon E. Schoenfield_, Jun 08 2007
%C A108825 a(35) > 13800000. - _Giovanni Resta_, Dec 21 2012
%e A108825 3! = 6; 6 mod 3 = 0.
%e A108825 9! = 362880; 3 + 6 + 2 + 8 + 8 = 27; 27 mod 9 = 0.
%e A108825 522 is a term because the digit sum of 522!, 4698, is divisible by 522.
%t A108825 Do[If[Mod[Plus @@ IntegerDigits[n! ], n] == 0, Print[n]], {n, 1, 10000}]
%Y A108825 Cf. A125526, A125724.
%K A108825 more,nonn,base
%O A108825 1,2
%A A108825 _Ryan Propper_, Jul 11 2005
%E A108825 a(20)-a(28) from _Ray Chandler_, Jul 25 2005
%E A108825 a(29)-a(31) from _Jon E. Schoenfield_, Jun 08 2007
%E A108825 Edited by _N. J. A. Sloane_, Jul 02 2008 at the suggestion of _R. J. Mathar_
%E A108825 a(32) from _Donovan Johnson_, Dec 08 2010
%E A108825 a(33)-a(34) from _Giovanni Resta_, Dec 21 2012