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

%I A135206 #27 Jun 18 2024 08:19:22
%S A135206 1,2,3,11,19,28,48,64,158,164,190,308,324,602,782,926,1202,1540,1568,
%T A135206 1614,2076,2122,2340,2546,2818,2858,2866,3334,3582,3714,4120,4266,
%U A135206 4794,5084,5432,5454,5696,6112,6250,6276,6358,6760,7368,8218,8970,9004,9088
%N A135206 Numbers m for which Sum_digits(m!) is a multiple of Sum_digits(m!!).
%H A135206 Michel Marcus, <a href="/A135206/b135206.txt">Table of n, a(n) for n = 1..90</a>
%e A135206 11!=11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)=36,
%e A135206 11!!=11*9*7*5*3*1=10395 -> (1+0+3+9+5)=18,
%e A135206 36/18=2.
%p A135206 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);
%t A135206 Select[Range[1000], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#!!, 10]]] &] (* _G. C. Greubel_, Sep 30 2016 *)
%o A135206 (PARI) df(n) = prod(i=0, (n-1)\2, n - 2*i ); \\ A006882
%o A135206 isok(m) = !(sumdigits(m!) % sumdigits(df(m))); \\ _Michel Marcus_, Jun 18 2024
%Y A135206 Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135204, A135205.
%K A135206 hard,nonn,base
%O A135206 1,2
%A A135206 _Paolo P. Lava_, Nov 30 2007
%E A135206 Changed offset to 1 by _Paolo P. Lava_, Jun 17 2024