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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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    http://oeis.org/A0021102011-04-24
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    http://en.wikipedia.org/wiki/Primorial2011-04-24
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    @quanta: That is not the same sequence. The sequence does, however, also appear at oeis: http://oeis.org/A076265 .2011-04-24
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    This is sequence A076265 on the OEIS, but while it is connected to a number of other sequences, there are no references listed.2011-04-24
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    If the sequence has yet to be named, I would probably use the name "hyperprimorial", by analogy with the usual [hyperfactorial](http://mathworld.wolfram.com/Hyperfactorial.html).2011-04-24

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