Let $a_1=1, a_n=(n-1)a_{n-1}+1,n\ge 2.$ Find $n$ such that $n|a_n.$

by Makar   Last Updated July 31, 2018 04:20 AM

Let $a_1=1, a_n=(n-1)a_{n-1}+1,n\ge 2.$ Find $n$ such that $n|a_n.$

My progress: Given recurrence can be rewritten as

$\frac{a_n}{(n-1)!}-\frac{a_{n-1}}{(n-2)!}=\frac{1}{(n-1)!}$

$\implies a_n=(n-1)!\sum_{k=0}^{n-1}\frac{1}{k!}$

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