A329039 If n = Product p_i^e_i, a(n) = n * Sum ((e_i - 1)/p_i).

0, 0, 0, 2, 0, 0, 0, 8, 3, 0, 0, 6, 0, 0, 0, 24, 0, 6, 0, 10, 0, 0, 0, 24, 5, 0, 18, 14, 0, 0, 0, 64, 0, 0, 0, 30, 0, 0, 0, 40, 0, 0, 0, 22, 15, 0, 0, 72, 7, 10, 0, 26, 0, 36, 0, 56, 0, 0, 0, 30, 0, 0, 21, 160, 0, 0, 0, 34, 0, 0, 0, 96, 0, 0, 15, 38, 0, 0, 0, 120, 81, 0, 0, 42, 0, 0, 0, 88, 0, 30, 0, 46, 0, 0, 0, 192, 0, 14, 33, 70, 0, 0, 0, 104, 0

Offset: 1

Author

Antti Karttunen, Nov 07 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A069359.

Cf. A005117 (positions of zeros).

Programs

PARI

A329039(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, ((f[i, 2]-1)/f[i, 1])));

Formula

a(n) = A003415(n) - A069359(n).