MathDB

Let

C=\{4,6,8,9,10,\ldots\}

be the set of composite positive integers. For each

n\in C

let

a_n

be the smallest positive integer

k

such that

k!

is divisible by

n

. Determine whether the following series converges:

\sum_{n\in C}\left(\frac{a_n}{n}\right)^n.

Proposed by Orif Ibrogimov, ETH Zurich and National University of Uzbekistan

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