## 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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