N5

Part of 2018-IMOC

Problems(1)

sum of squares of divisors of k,n is n,k for all n

Source: IMOC 2018 N5

Find all positive integers

k

such that for every

n\in\mathbb N

k

factors (not necessarily distinct) of

n

so that the sum of their squares is

n

, then there are

k

factors (not necessarily distinct) of

n

so that their sum is exactly

n