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nice question 2

Source: iran tst 2014 third exam

May 22, 2014
functionnumber theoryprime numbersnumber theory proposed

Problem Statement

is there a function f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} such that i)∃n∈N:f(n)≠ni) \exists n\in \mathbb{N}:f(n)\neq n ii)ii) the number of divisors of mm is f(n)f(n) if and only if the number of divisors of f(m)f(m) is nn
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