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A109491 Value of Product_{k=1..n} sigma(k)/sd(k,2), where sd(k,b) is the sum of the digits of k represented in base b.

%I A109491 #17 Jan 22 2018 22:36:04
%S A109491 1,3,6,42,126,756,2016,30240,196560,1769040,7076160,99066240,
%T A109491 462309120,3698472960,22190837760,687915970560,6191243735040,
%U A109491 120729252833280,804861685555200,16902095396659200,180289017564364800
%N A109491 Value of Product_{k=1..n} sigma(k)/sd(k,2), where sd(k,b) is the sum of the digits of k represented in base b.
%C A109491 Surprisingly, the product in the definition is an integer for all values of n for which it has been calculated (1-300), whereas the corresponding base-3 product is not.
%C A109491 The product is an integer at least for n <= 80000. - _Robert Israel_, Jan 22 2018
%H A109491 Robert Israel, <a href="/A109491/b109491.txt">Table of n, a(n) for n = 1..534</a>
%e A109491 The divisors of 1-5 are {1}, {1,2}, {1,3}, {1,2,4} and {1,5}, respectively and the base-2 representations of 1-5 are 1,10,11,100,101, so a(5)=(1/1)(3/1)(4/2)(7/1)(6/2)=126.
%p A109491 p:= 1: A[1]:= 1:
%p A109491 for n from 2 to 50 do
%p A109491 p:= p * numtheory:-sigma(n)/convert(convert(n,base,2),`+`);
%p A109491 A[n]:= p;
%p A109491 od:
%p A109491 seq(A[i],i=1..50); # _Robert Israel_, Jan 22 2018
%o A109491 (PARI) a(n) = prod(k=1, n, sigma(k)/hammingweight(k)); \\ _Michel Marcus_, Jul 10 2014
%Y A109491 Cf. A109489.
%K A109491 nonn,base
%O A109491 1,2
%A A109491 _John W. Layman_, Jun 29 2005
%E A109491 Offset corrected to 1 by _Michel Marcus_, Jul 10 2014