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

Offset: 1

Author

Reinhard Zumkeller, May 03 2013

Keywords

• sign

Links

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

Crossrefs

Cf. A001221, A051903.

Cf. A188654, A212164, A212165, A212166, A212167, A212168.

Programs

Haskell

a225230 n = a001221 n - a051903 n

Mathematica

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

PARI

a(n) = if (n>1, my(f=factor(n)); #f~ - vecmax(f[,2]), 0); \\ Michel Marcus, Jan 26 2022

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.