OFFSET
1,2
COMMENTS
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.
The product is an integer at least for n <= 80000. - Robert Israel, Jan 22 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..534
EXAMPLE
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.
MAPLE
p:= 1: A[1]:= 1:
for n from 2 to 50 do
p:= p * numtheory:-sigma(n)/convert(convert(n, base, 2), `+`);
A[n]:= p;
od:
seq(A[i], i=1..50); # Robert Israel, Jan 22 2018
PROG
(PARI) a(n) = prod(k=1, n, sigma(k)/hammingweight(k)); \\ Michel Marcus, Jul 10 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
John W. Layman, Jun 29 2005
EXTENSIONS
Offset corrected to 1 by Michel Marcus, Jul 10 2014
STATUS
approved