## Prime factors of `n`^{15}+1

### Problem 421

Published on Sunday, 31st March 2013, 04:00 am; Solved by 309; Difficulty rating: 50%
Numbers of the form `n`^{15}+1 are composite for every integer `n` > 1.

For positive integers `n` and `m` let `s`(`n,m`) be defined as the sum of the *distinct* prime factors of `n`^{15}+1 not exceeding `m`.

^{15}+1 = 3×3×11×331.

So

`s`(2,10) = 3 and

`s`(2,1000) = 3+11+331 = 345.

Also 10

^{15}+1 = 7×11×13×211×241×2161×9091.

So

`s`(10,100) = 31 and

`s`(10,1000) = 483.

Find ∑ `s`(`n`,10^{8}) for 1 ≤ `n` ≤ 10^{11}.