A349391 Dirichlet convolution of A126760 with omega.

0, 1, 1, 2, 1, 4, 1, 3, 2, 5, 1, 7, 1, 6, 5, 4, 1, 7, 1, 9, 6, 7, 1, 10, 3, 8, 3, 11, 1, 16, 1, 5, 7, 9, 7, 12, 1, 10, 8, 13, 1, 20, 1, 13, 9, 11, 1, 13, 4, 18, 9, 15, 1, 10, 8, 16, 10, 13, 1, 27, 1, 14, 11, 6, 9, 24, 1, 17, 11, 32, 1, 17, 1, 16, 18, 19, 9, 28, 1, 17, 4, 17, 1, 34, 10, 18, 13, 19, 1, 27, 10, 21

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n} A126760(n/d) * A001221(d).

Mathematica

f[n_] := 2 * Floor[(m = n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3])/6] + Mod[m, 3]; a[n_] := DivisorSum[n, f[#] * PrimeNu[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

Prog

(PARI)
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
A349391(n) = sumdiv(n, d, A126760(n/d)*omega(d));

Crossrefs

Cf. A001221, A126760.

Cf. A347233, A347234, A349390, A349392, A349393, A349395 for other Dirichlet convolutions of A126760. And also A347957.

Sequence in context: A263653 A330328 A269427 * A077808 A021471 A088372

Adjacent sequences: A349388 A349389 A349390 * A349392 A349393 A349394

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved