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Edit: I'm shifting to a more general question:
If the prime factorization of an integer n is given by
n = p1v1p2v2⋅⋅⋅pkvk
then what would be a proof for the number of positive divisors of n being
d(n) = (v1 + 1)(v2 + 1)⋅⋅⋅(vk + 1)
If the prime factorization of an integer n is given by
n = p1v1p2v2⋅⋅⋅pkvk
then what would be a proof for the number of positive divisors of n being
d(n) = (v1 + 1)(v2 + 1)⋅⋅⋅(vk + 1)
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