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Sum of distinct prime divisors

Source: IZHO 2017 day p5

January 15, 2017
number theoryprimesDivisors

Problem Statement

For each positive integer kk denote C(k)C(k) to be sum of its distinct prime divisors. For example C(1)=0,C(2)=2,C(45)=8C(1)=0,C(2)=2,C(45)=8. Find all positive integers nn for which C(2n+1)=C(n)C(2^n+1)=C(n).
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