A135206 Numbers n for which Sum_digits(n!) is a multiple of Sum_digits(n!!).

1, 2, 3, 11, 19, 28, 48, 64, 158, 164, 190, 308, 324, 602, 782, 926, 1202, 1540, 1568, 1614, 2076, 2122, 2340, 2546, 2818, 2858, 2866, 3334, 3582, 3714, 4120, 4266, 4794, 5084, 5432, 5454, 5696, 6112, 6250, 6276, 6358, 6760, 7368, 8218, 8970, 9004, 9088

Offset

0,2

Links

Table of n, a(n) for n=0..46.

Example

11!=11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)=36,
11!!=11*9*7*5*3*1=10395 -> (1+0+3+9+5)=18,
36/18=2.

Maple

P:=proc(n) local i, j, 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:=i; j:=i-2; while j >0 do x:=x*j; j:=j-2; od: k:=x; x:=0; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(w/x)=w/x then print(i); fi; od; end: P(1000);

Mathematica

Select[Range[1000], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#!!, 10]]] &] (* G. C. Greubel, Sep 30 2016 *)

Crossrefs

Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135204, A135205.

Sequence in context: A172258 A306395 A363497 * A368278 A235629 A111802

Adjacent sequences: A135203 A135204 A135205 * A135207 A135208 A135209

Keyword

hard,nonn,base

Author

Paolo P. Lava, Nov 30 2007

Status

approved