A078771 a(n) = A008475(n) - A001414(n).

0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 8, 0, 3, 0, 0, 0, 0, 0, 2, 15, 0, 18, 0, 0, 0, 0, 22, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 8, 35, 15, 0, 0, 0, 18, 0, 2, 0, 0, 0, 0, 0, 0, 3, 52, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 15, 0, 0, 0, 0, 8, 69, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 22, 0, 35, 3, 15

Offset: 1

Author

Benoit Cloitre, Jan 11 2003

Keywords

• nonn

Comments

a(n) is not zero if n is in A046790.

Links

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

Crossrefs

Cf. A001414, A008475, A046790.

Programs

Mathematica

Array[Total[Power @@@ #] - Total[Times @@@ #] &@ FactorInteger@ # &, 100] (* Michael De Vlieger, Nov 17 2017, after Olivier Gérard at A008475 and Ray Chandler at A001414 *)

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ This function from M. F. Hasler, Feb 07 2009
A008475(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^f[i,2])); };
A078771(n) = (A008475(n) - A001414(n)); \\ Antti Karttunen, Nov 17 2017

PARI

a(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i,1]^f[i,2] - f[i,1]*f[i,2]);} \\ Amiram Eldar, May 03 2025

Formula

Additive with a(p^e) = p^e - p*e. - Amiram Eldar, May 03 2025