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A108825 Numbers n such that n divides the sum of the digits of n!. 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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..34.

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.

MAPLE

P:=proc(n) local i, k, w; for i from 1 by 1 to n do w:=0; k:=i!; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if (w mod i)=0 then print(i); fi; od; end: P(700); # Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007

MATHEMATICA

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

CROSSREFS

Cf. A125526, A125724.

Sequence in context: A083303 A245594 A078610 * A109663 A056702 A294126

Adjacent sequences:  A108822 A108823 A108824 * A108826 A108827 A108828

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

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)