A347954 Dirichlet convolution of A003602 with A342001.

0, 1, 1, 3, 1, 8, 1, 6, 4, 11, 1, 20, 1, 14, 13, 10, 1, 26, 1, 29, 16, 20, 1, 37, 5, 23, 12, 38, 1, 81, 1, 15, 22, 29, 19, 62, 1, 32, 25, 55, 1, 106, 1, 56, 48, 38, 1, 59, 6, 48, 31, 65, 1, 74, 25, 73, 34, 47, 1, 191, 1, 50, 61, 21, 28, 156, 1, 83, 40, 151, 1, 112, 1, 59, 60, 92, 28, 181, 1, 89, 34, 65, 1, 254, 34

Offset: 1

Author

Antti Karttunen, Sep 20 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A003557, A003602, A342001.

Cf. also A347234, A347955, A347956.

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]));
A003602(n) = (1+(n>>valuation(n,2)))/2;
A342001(n) = (A003415(n) / A003557(n));
A347954(n) = sumdiv(n,d,A003602(d)*A342001(n/d));

Formula

a(n) = Sum_{d|n} A003602(d) * A342001(n/d).