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

1,4

Links

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

Jon Maiga, Computer-generated formulas for A347957, Sequence Machine.

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)

Prog

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

Crossrefs

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

Cf. also A328203, A347954, A347955, A347956.

Sequence in context: A332085 A055205 A342001 * A377801 A369038 A161686

Adjacent sequences: A347954 A347955 A347956 * A347958 A347959 A347960

Keyword

nonn

Author

Antti Karttunen, Sep 20 2021

Status

approved