Freaky Function!

Algebra Level 3

A function f:NNf: \mathbb{N} \rightarrow \mathbb{N} is such that

1) f(xy)=f(x)f(y)f(xy)= f(x)f(y)

2) The function is strictly increasing.

3) f(2)=2f(2)=2

Find k=120f(k)\sum _{ k=1 }^{ 20 }{ f(k) }

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