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

1,2

Links

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

Formula

a(n) = Sum_{d|n} A126760(n/d) * A000005(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[#] * DivisorSigma[0, 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
A349392(n) = sumdiv(n, d, A126760(n/d)*numdiv(d));

Crossrefs

Cf. A000005, A126760.

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

Sequence in context: A135986 A334848 A284614 * A069734 A265703 A070952

Adjacent sequences: A349389 A349390 A349391 * A349393 A349394 A349395

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved