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MAA finally wrote sum good number theory

Source: 2021 AIME I P14

March 11, 2021
number theory2021 AIME I

Problem Statement

For any positive integer a,a, σ(a)\sigma(a) denotes the sum of the positive integer divisors of a.a. Let nn be the least positive integer such that σ(an)−1\sigma(a^n)-1 is divisible by 20212021 for all positive integers a.a. Find the sum of the prime factors in the prime factorization of n.n.
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