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A108825
Numbers j such that j divides the sum of the digits of j!.
5
1, 2, 3, 9, 15, 18, 21, 27, 72, 81, 234, 462, 502, 522, 1314, 1323, 3789, 3897, 6462, 10470, 17532, 17820, 28503, 48248, 48254, 48303, 48644, 48856, 223551, 226149, 227406, 625986, 4838918, 4848004
OFFSET
1,2
COMMENTS
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
a(35) > 13800000. - Giovanni Resta, Dec 21 2012
EXAMPLE
3! = 6; 6 mod 3 = 0.
9! = 362880; 3 + 6 + 2 + 8 + 8 = 27; 27 mod 9 = 0.
522 is a term because the digit sum of 522!, 4698, is divisible by 522.
MATHEMATICA
Do[If[Mod[Plus @@ IntegerDigits[n! ], n] == 0, Print[n]], {n, 1, 10000}]
CROSSREFS
Sequence in context: A083303 A245594 A078610 * A109663 A056702 A294126
KEYWORD
more,nonn,base
AUTHOR
Ryan Propper, Jul 11 2005
EXTENSIONS
a(20)-a(28) from Ray Chandler, Jul 25 2005
a(29)-a(31) from Jon E. Schoenfield, Jun 08 2007
Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar
a(32) from Donovan Johnson, Dec 08 2010
a(33)-a(34) from Giovanni Resta, Dec 21 2012
STATUS
approved