Question about A052130
- Sloane's A052130 is generated as follows:
a(n) = number of numbers between 1 and 2^m with m-n prime
factors (counted with multiplicity). . . .
a(n) = number of products of half-odd-primes <= 2^n. E.g. a(2) = 7
since 1, 3/2, (3/2)^2, (3/2)^3, (3/2)*(5/2), 5/2, 7/2 are all <= 2^2
I'm curious as to why this is the case; i.e., why the number of
integers with m-n prime factors would be equal to then number of half-
odd-primes <= 2^n. Again, my Google skills have failed me in looking
for an answer. Could someone point me in the right direction?
Here's the full link to the sequence from the online integer database: