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.

1, 3, 6, 42, 126, 756, 2016, 30240, 196560, 1769040, 7076160, 99066240, 462309120, 3698472960, 22190837760, 687915970560, 6191243735040, 120729252833280, 804861685555200, 16902095396659200, 180289017564364800

Offset: 1

Author

John W. Layman, Jun 29 2005

Keywords

• nonn
• base

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

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..534

Crossrefs

Cf. A109489.

Programs

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

PARI

a(n) = prod(k=1, n, sigma(k)/hammingweight(k)); \\ Michel Marcus, Jul 10 2014

Extensions

Offset corrected to 1 by Michel Marcus, Jul 10 2014