A349392 Dirichlet convolution of A126760 with tau (number of divisors function).

1, 3, 3, 6, 4, 9, 5, 10, 6, 12, 6, 18, 7, 15, 12, 15, 8, 18, 9, 24, 15, 18, 10, 30, 16, 21, 10, 30, 12, 36, 13, 21, 18, 24, 26, 36, 15, 27, 21, 40, 16, 45, 17, 36, 24, 30, 18, 45, 26, 48, 24, 42, 20, 30, 35, 50, 27, 36, 22, 72, 23, 39, 30, 28, 40, 54, 25, 48, 30, 78, 26, 60, 27, 45, 48, 54, 44, 63, 29, 60, 15, 48

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000005, A126760.

Cf. A347233, A347234, A349390, A349391, A349393, A349395 for other Dirichlet convolutions of A126760. And also A349372.

Programs

Mathematica

f[n_] := 2 * Floor[(m = n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3])/6] + Mod[m, 3]; a[n_] := DivisorSum[n, f[#] * DivisorSigma[0, n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

PARI

A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A349392(n) = sumdiv(n,d,A126760(n/d)*numdiv(d));

Formula

a(n) = Sum_{d|n} A126760(n/d) * A000005(d).