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Denote the elementary symmetric functions in $n$ variables by $e_k(x_1, x_2,\dots, x_n)$. In the special case $x_j=j$, simply write $e_k(n)$ for $e_k(1, 2, \dots, n)$. Next, define the sequence $$a_{+}...

I have no experience with this, so I dont know if this is too easy for MO. Let $(a_n)$ be a strictly monotone sequence of natural numbers, then define the set of nice numbers of $(a_n)$ as $X(a_n):=\{...