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A109489 Value of Product[k/sd(k,2),k=1..n], where sd(k,b) is the sum of the digits of k represented in base b.

%I A109489 #12 Jan 22 2018 03:05:47
%S A109489 1,2,3,12,30,90,210,1680,7560,37800,138600,831600,3603600,16816800,
%T A109489 63063000,1009008000,8576568000,77189112000,488864376000,
%U A109489 4888643760000,34220506320000,250950379680000,1442964683160000,17315576197920000
%N A109489 Value of Product[k/sd(k,2),k=1..n], where sd(k,b) is the sum of the digits of k represented in base b.
%C A109489 It appears that Product[k/sd(k,b),k=1..n] is an integer for all integers n>0 and b>1. Is this known or easy to prove?
%C A109489 It is not true!  The product is not an integer for b=2 and n=422 (it has a denominator of 5).  B-file contains all terms before that. - _Robert Israel_, Jan 21 2018
%H A109489 Robert Israel, <a href="/A109489/b109489.txt">Table of n, a(n) for n = 1..421</a>
%e A109489 The base 2 representations of 1,2,3,4 are 1,10,11,100 so a(4)=(1/1)(2/1)(3/2)(4/1)=12.
%p A109489 P:= 1: A[1]:= P:
%p A109489 for n from 2 to 100 do
%p A109489   P:= P*n/convert(convert(n,base,2),`+`);
%p A109489   A[n]:= P;
%p A109489 od:
%p A109489 seq(A[i],i=1..100); # _Robert Israel_, Jan 21 2018
%o A109489 (PARI) a(n) = prod(k=1, n, k/hammingweight(k)); \\ _Michel Marcus_, Jul 10 2014
%Y A109489 Cf. A003601, A109490, A109491, A109492.
%K A109489 nonn,base,fini
%O A109489 1,2
%A A109489 _John W. Layman_, Jun 29 2005