A081805 a(n) = n minus (largest prime power in n factorization); a(1) = 0.

0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 8, 0, 7, 10, 0, 0, 9, 0, 15, 14, 11, 0, 16, 0, 13, 0, 21, 0, 25, 0, 0, 22, 17, 28, 27, 0, 19, 26, 32, 0, 35, 0, 33, 36, 23, 0, 32, 0, 25, 34, 39, 0, 27, 44, 48, 38, 29, 0, 55, 0, 31, 54, 0, 52, 55, 0, 51, 46, 63, 0, 63, 0, 37, 50, 57, 66, 65, 0, 64, 0, 41, 0

Offset: 1

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

Comments

a(n) = 0 when n is a prime power (A000961). - Michel Marcus, Dec 03 2013

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A034699, A052128, A284600.

Programs

Mathematica

f[n_] := (n - (#[[1]]^#[[2]]) & /@ {FactorInteger[n][[-1]] })[[1]]; Array[f, 80] (* Robert G. Wilson v, Aug 07 2018 *)

PARI

A081805(n) = if(1==n,0,my(f = factor(n)); n - vecmax(vector(#f~, k, f[k, 1]^f[k, 2]))); \\ Michel Marcus Jul 24 2017 & Antti Karttunen, Aug 06 2018

Formula

a(n) = n - A034699(n). - Michel Marcus, Jul 24 2017

Extensions

Term a(1) = 0 prepended by Antti Karttunen, Aug 06 2018