A225230 - OEIS

A225230

In the canonical prime factorization of n: (number of distinct primes) minus (largest prime exponent).

0, 0, 0, -1, 0, 1, 0, -2, -1, 1, 0, 0, 0, 1, 1, -3, 0, 0, 0, 0, 1, 1, 0, -1, -1, 1, -2, 0, 0, 2, 0, -4, 1, 1, 1, 0, 0, 1, 1, -1, 0, 2, 0, 0, 0, 1, 0, -2, -1, 0, 1, 0, 0, -1, 1, -1, 1, 1, 0, 1, 0, 1, 0, -5, 1, 2, 0, 0, 1, 2, 0, -1, 0, 1, 0, 0, 1, 2, 0, -2, -3

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OFFSET

1,8

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001221(n) - A051903(n).

a(A212164(n)) < 0; a(A212165(n)) <= 0; a(A212166(n)) = 0; a(A188654(n)) <> 0; a(A212167(n)) >= 0; a(A212168(n)) > 0.

MATHEMATICA

a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Length[e] - Max[e]]; Array[a, 100] (* Amiram Eldar, Sep 09 2024 *)

PROG

(Haskell)