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

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

Author

Ryan Propper, Jul 11 2005

Keywords

• more
• nonn
• base

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

Examples

			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.
		

Crossrefs

Cf. A125526, A125724.

Programs

Mathematica

Do[If[Mod[Plus @@ IntegerDigits[n! ], n] == 0, Print[n]], {n, 1, 10000}]

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