A135204 Numbers n for which Sum_digits(n!) is a multiple of Sum_digits(n).

1, 2, 3, 9, 10, 11, 12, 14, 16, 18, 20, 21, 22, 27, 28, 30, 33, 35, 36, 44, 45, 51, 54, 60, 61, 63, 72, 75, 81, 87, 90, 99, 100, 102, 105, 108, 111, 114, 117, 120, 126, 130, 135, 143, 144, 153, 158, 162, 165, 171, 180, 182, 185, 189, 190, 192, 200, 201, 202, 204, 206

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 30 2007

Keywords

• nonn
• base

Comments

I expect a(n) to be around kn log n for some constant k. - Charles R Greathouse IV, Apr 24 2013

Examples

			11 -> 11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)/(1+1)=18.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135205, A135206.

Programs

Maple

P:=proc(n) local i,k,w,x; 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; x:=0; k:=i!; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(x/w)=x/w then print(i); fi; od; end: P(1000);

Mathematica

Select[Range[100], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#, 10]]] &] (* G. C. Greubel, Sep 30 2016 *)

PARI

is(n)=sumdigits(n!)%sumdigits(n)==0 \\ Charles R Greathouse IV, Apr 24 2013