A370328 - OEIS

A370328

The number of powerful divisors of the powerful numbers.

1, 2, 3, 2, 4, 2, 3, 5, 4, 2, 6, 6, 4, 4, 6, 2, 3, 7, 8, 2, 4, 6, 9, 4, 5, 8, 10, 2, 8, 3, 2, 6, 8, 12, 4, 4, 6, 9, 2, 12, 4, 12, 6, 4, 6, 8, 10, 2, 15, 8, 2, 6, 10, 9, 10, 4, 6, 14, 4, 4, 16, 6, 3, 6, 2, 6, 4, 4, 10, 12, 2, 18, 8, 12, 2, 8, 15, 12, 8, 11, 4, 7

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OFFSET

1,2

COMMENTS

The product of the exponents of the prime factorization of the powerful numbers.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A005361(A001694(n)).

a(n) = A000005(A306458(n)).

MATHEMATICA

f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[n == 1 || Min[e] > 1, Times @@ e, Nothing]]; Array[f, 2500]