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I'm going to tag this as reference request, since I'm mainly interested in finding out whether this kind of sequence has been named in literature before, just in order to acknowledge it for something I am working on.

The sequence is the following, $$ a_n = \prod^n p_{i}^{p_i}$$

for $n \geq 1$ where $p_i$ is the $i$-th prime number. So it's basically the sequence of integers of prime factors to the power of themselves, i.e. $2^2,2^2 3^3, 2^2 3^3 5^5$ and so on.

Do you know is this has been studied? If yes, could you recommend any interesting literature on it?

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  • $\begingroup$ oeis.org/A002110 $\endgroup$ – quanta Apr 24 '11 at 12:47
  • $\begingroup$ en.wikipedia.org/wiki/Primorial $\endgroup$ – quanta Apr 24 '11 at 12:48
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    $\begingroup$ @quanta: That is not the same sequence. The sequence does, however, also appear at oeis: oeis.org/A076265 . $\endgroup$ – Raeder Apr 24 '11 at 12:51
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    $\begingroup$ This is sequence A076265 on the OEIS, but while it is connected to a number of other sequences, there are no references listed. $\endgroup$ – Arturo Magidin Apr 24 '11 at 12:51
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    $\begingroup$ If the sequence has yet to be named, I would probably use the name "hyperprimorial", by analogy with the usual hyperfactorial. $\endgroup$ – J. M. is a poor mathematician Apr 24 '11 at 13:31

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