A task regarding the R-sequence research

I came up with this task two days ago. Then had to sleep over the idea to write this down here. Now, waiting for your insights.

Let P={p_1,p_2,…,p_n}, for n \in N, be set of primes. Find the number of combinations of elements of P out of which we can build a k-divisor number (by multiplying the chosen numbers), k\in N. Divisors within a number don’t need to be distinct.

Example: For {3,5,7,11,13}, we have for k=3 e.g. (3,5,11) or (7,11,13), but also (3,3,5), (3,3,3). For k=4 we could have e.g.(3,7,11,13) or (7,7,13,13).

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Another thing, I recently played a little with a function: f(n) = \sum\limits_{p\le n}{{{n}\choose{p}}}, n \in N and noticed that for prime n, the result of the function cannot be prime. Then wanted to think that it might be interesting to investigate this function only for prime n.

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About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
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