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sum of squares of its proper divisors is equal to 2n+4

Source: 2009 Argentina OMA Finals L3 p2

January 15, 2023

number theoryDivisors

Problem Statement

A positive integer

n

is acceptable if the sum of the squares of its proper divisors is equal to

2n+4

(a divisor of

n

is proper if it is different from

1

and of

n

). Find all acceptable numbers less than

10000