OFFSET
1,2
COMMENTS
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?
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
LINKS
Robert Israel, Table of n, a(n) for n = 1..421
EXAMPLE
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.
MAPLE
P:= 1: A[1]:= P:
for n from 2 to 100 do
P:= P*n/convert(convert(n, base, 2), `+`);
A[n]:= P;
od:
seq(A[i], i=1..100); # Robert Israel, Jan 21 2018
PROG
(PARI) a(n) = prod(k=1, n, k/hammingweight(k)); \\ Michel Marcus, Jul 10 2014
CROSSREFS
KEYWORD
nonn,base,fini
AUTHOR
John W. Layman, Jun 29 2005
STATUS
approved