[seqfan] n = Product derived from binary representation of n

[Leroy Quet]

Let b(n,k) = the kth binary digit (starting at k=1, reading right to left) in the base 2 representation of n.

So: n = sum{k>=0} b(k+1)*2^k.


Consider the sequence of those positive integers n where:

n = product{k>=1} k^b(n,k).

Example: 12 in binary is 1100. And 12 = 4^1 * 3^1 * 2^0 * 1^0.

The sequence of such n's begins: 1,2,6,12.

Does this sequence continue? Is it finite or infinite? And is it already in the EIS?

A search for acceptable n's can be sped up by noting that if an integer n is such that 2^(m-1) <= n <= 2^m - 1, then only multiples of m need to be checked in that range because the mth digit from the right (ie, the leftmost digit 1) is inevitably 1, thus the product contains the factor m.

Thanks,
Leroy Quet