A368925 - OEIS

A368925

The minimal exponent in the prime factorization of the powerful numbers.

0, 2, 3, 2, 4, 2, 3, 5, 2, 2, 6, 2, 4, 2, 2, 2, 3, 7, 2, 2, 2, 2, 3, 2, 5, 8, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 9, 2, 2, 4, 3, 2, 2, 6, 2, 2, 2, 3, 2, 2, 2, 2, 3, 10, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 11, 2, 7, 3, 2, 2, 2, 4

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OFFSET

1,2

LINKS

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

FORMULA

a(n) = A051904(A001694(n)).

a(n) >= 2 for n >= 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2.

MATHEMATICA

s[n_] := If[n == 1, 0, Min @@ Last /@ FactorInteger[n]]; s /@ Select[Range[3000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]

(* or *)