A347957 Dirichlet convolution of A001221 (omega) with A003602 (Kimberling's paraphrases).

0, 1, 1, 2, 1, 5, 1, 3, 3, 6, 1, 9, 1, 7, 7, 4, 1, 14, 1, 11, 8, 9, 1, 13, 4, 10, 8, 13, 1, 28, 1, 5, 10, 12, 9, 25, 1, 13, 11, 16, 1, 34, 1, 17, 22, 15, 1, 17, 5, 25, 13, 19, 1, 38, 11, 19, 14, 18, 1, 49, 1, 19, 26, 6, 12, 46, 1, 23, 16, 44, 1, 36, 1, 22, 31, 25, 12, 52, 1, 21, 22, 24, 1, 60, 14, 25, 19, 25, 1, 86

Offset: 1

Author

Antti Karttunen, Sep 20 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Jon Maiga, Computer-generated formulas for A347957, Sequence Machine.

Crossrefs

Cf. A001221, A003602, A023900, A181988, A205745.

Cf. also A328203, A347954, A347955, A347956.

Programs

PARI

A003602(n) = (1+(n>>valuation(n,2)))/2;
A347957(n) = sumdiv(n,d,omega(n/d)*A003602(d));

Formula

a(n) = Sum_{d|n} A001221(n/d) * A003602(d).

From Antti Karttunen, Nov 13 2021: (Start)

The following two convolutions were found by Jon Maiga's Sequence Machine search algorithm. The first one is obvious, and even the second one should not be too hard to prove:

a(n) = Sum_{d|n} A023900(n/d) * A347956(d).

a(n) = Sum_{d|n} A181988(n/d) * A205745(d).

(End)