[seqfan] A Product of Prime Powers.

[Peter Luschny]

There is a curious little sequence which I try to understand better.

a(n) = 1,2,3,2,5,3,7,4,1,5,11,9,13,7,1,16,17,1,19,25,1,11,23,81,1,13,...

Only 1 or powers of primes occur, and in the latter case the prime
is a factor of n. Now let's look at the partial products of a(n):

p(n) = 1,2,6,12,60,180,1260,5040,5040,25200,277200,2494800,...

This sequence has an interesting representation:

p(n) = product(prim(n,i)^(2^i), i=0..A059939(n))

where prim(n,i) is the product of the primes in the interval
J(n, i) = [floor(n/2^(i+1))+1, floor(n/2^i)].

(For example prim(n,0) is A055773.)

My question is: How can a(n) be defined best?

Cheers, Peter