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.

1, 2, 3, 12, 30, 90, 210, 1680, 7560, 37800, 138600, 831600, 3603600, 16816800, 63063000, 1009008000, 8576568000, 77189112000, 488864376000, 4888643760000, 34220506320000, 250950379680000, 1442964683160000, 17315576197920000

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

Cf. A003601, A109490, A109491, A109492.

Sequence in context: A247651 A305746 A221510 * A169636 A105401 A325595

Adjacent sequences: A109486 A109487 A109488 * A109490 A109491 A109492

Keyword

nonn,base,fini

Author

John W. Layman, Jun 29 2005

Status

approved