cp's OEIS Frontend

A135205 Numbers m for which Sum_digits(m!!) is a multiple of Sum_digits(m).

%I A135205 #18 Jun 18 2024 08:19:51
%S A135205 1,2,3,4,6,9,10,11,12,15,18,20,21,24,25,27,30,32,33,36,42,45,46,54,55,
%T A135205 63,72,75,81,88,90,91,93,100,101,102,105,108,111,112,117,120,121,122,
%U A135205 123,124,126,127,135,141,144,153,154,156,162,171,176,180,182,189,198
%N A135205 Numbers m for which Sum_digits(m!!) is a multiple of Sum_digits(m).
%H A135205 G. C. Greubel, <a href="/A135205/b135205.txt">Table of n, a(n) for n = 1..1000</a>
%e A135205 11 -> 11*9*7*5*3*1=10395 -> (1+0+3+9+5)/(1+1) = 9.
%p A135205 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(x/w)=x/w then print(i); fi; od; end: P(1000);
%t A135205 Select[Range[100], Divisible[Total[IntegerDigits[#!!, 10]], Total[IntegerDigits[#, 10]]] &] (* _G. C. Greubel_, Sep 30 2016 *)
%Y A135205 Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135204, A135206.
%K A135205 easy,nonn,base
%O A135205 1,2
%A A135205 _Paolo P. Lava_, Nov 30 2007
%E A135205 Offset 1 and b-file adapted by _Paolo P. Lava_, Jun 17 2024