A347963 Dirichlet convolution of A342001 with A003557.

0, 1, 1, 3, 1, 7, 1, 7, 3, 9, 1, 18, 1, 11, 10, 15, 1, 18, 1, 24, 12, 15, 1, 40, 3, 17, 8, 30, 1, 54, 1, 31, 16, 21, 14, 45, 1, 23, 18, 54, 1, 68, 1, 42, 27, 27, 1, 84, 3, 24, 22, 48, 1, 48, 18, 68, 24, 33, 1, 132, 1, 35, 33, 63, 20, 96, 1, 60, 28, 90, 1, 99, 1, 41, 27, 66, 20, 110, 1, 114, 22, 45, 1, 168, 24, 47

Offset: 1

Author

Antti Karttunen, Sep 24 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003415, A003557, A342001.

Cf. also A347961.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A347963(n) = sumdiv(n,d,A003557(n/d)*A342001(d));

Formula

a(n) = Sum_{d|n} A003557(d) * A342001(n/d).