A347955 Dirichlet convolution of A003415 (arithmetic derivative) with A003602 (Kimberling's paraphrases).

0, 1, 1, 5, 1, 8, 1, 17, 8, 11, 1, 32, 1, 14, 13, 49, 1, 44, 1, 47, 16, 20, 1, 100, 13, 23, 44, 62, 1, 81, 1, 129, 22, 29, 19, 156, 1, 32, 25, 151, 1, 106, 1, 92, 86, 38, 1, 276, 18, 92, 31, 107, 1, 206, 25, 202, 34, 47, 1, 301, 1, 50, 111, 321, 28, 156, 1, 137, 40, 151, 1, 460, 1, 59, 120, 152, 28, 181, 1, 423, 206

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, A003602.

Cf. also A347954, A347956.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003602(n) = (1+(n>>valuation(n,2)))/2;
A347955(n) = sumdiv(n,d,A003415(n/d)*A003602(d));

Formula

a(n) = Sum_{d|n} A003415(n/d) * A003602(d).