

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.


3



1, 2, 3, 12, 30, 90, 210, 1680, 7560, 37800, 138600, 831600, 3603600, 16816800, 63063000, 1009008000, 8576568000, 77189112000, 488864376000, 4888643760000, 34220506320000, 250950379680000, 1442964683160000, 17315576197920000
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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). Bfile contains all terms before that.  Robert Israel, Jan 21 2018


LINKS



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:


PROG

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


CROSSREFS



KEYWORD

nonn,base,fini


AUTHOR



STATUS

approved



