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Prime factors of n15+1

Problem 421

Published on 31 March 2013 at 04:00 am [Server Time]

Numbers of the form n15+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 n15+1 not exceeding m.

E.g. 215+1 = 3×3×11×331.
So s(2,10) = 3 and s(2,1000) = 3+11+331 = 345.

Also 1015+1 = 7×11×13×211×241×2161×9091.
So s(10,100) = 31 and s(10,1000) = 483.

Find ∑ s(n,108) for 1 ≤ n ≤ 1011.


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