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

%I A135204 #19 Oct 01 2016 16:09:15
%S A135204 1,2,3,9,10,11,12,14,16,18,20,21,22,27,28,30,33,35,36,44,45,51,54,60,
%T A135204 61,63,72,75,81,87,90,99,100,102,105,108,111,114,117,120,126,130,135,
%U A135204 143,144,153,158,162,165,171,180,182,185,189,190,192,200,201,202,204,206
%N A135204 Numbers n for which Sum_digits(n!) is a multiple of Sum_digits(n).
%C A135204 I expect a(n) to be around kn log n for some constant k. - _Charles R Greathouse IV_, Apr 24 2013
%H A135204 G. C. Greubel, <a href="/A135204/b135204.txt">Table of n, a(n) for n = 1..1000</a>
%e A135204 11 -> 11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)/(1+1)=18.
%p A135204 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);
%t A135204 Select[Range[100], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#, 10]]] &] (* _G. C. Greubel_, Sep 30 2016 *)
%o A135204 (PARI) is(n)=sumdigits(n!)%sumdigits(n)==0 \\ _Charles R Greathouse IV_, Apr 24 2013
%Y A135204 Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135205, A135206.
%K A135204 nonn,base
%O A135204 1,2
%A A135204 _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 30 2007