A349390 Dirichlet convolution of A126760 with Kimberling's paraphrases, A003602.

1, 2, 3, 3, 5, 6, 7, 4, 8, 10, 10, 9, 12, 14, 17, 5, 15, 16, 17, 15, 24, 20, 20, 12, 28, 24, 22, 21, 25, 34, 27, 6, 35, 30, 47, 24, 32, 34, 42, 20, 35, 48, 37, 30, 50, 40, 40, 15, 54, 56, 53, 36, 45, 44, 71, 28, 60, 50, 50, 51, 52, 54, 71, 7, 84, 70, 57, 45, 71, 94, 60, 32, 62, 64, 100, 51, 99, 84, 67, 25, 63, 70, 70

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A126760(n/d) * A003602(d).

Mathematica

f[n_] := 2 * Floor[(m = n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3])/6] + Mod[m, 3]; k[n_] := (n/2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, f[#] * k[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)

Prog

(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
A349390(n) = sumdiv(n, d, A126760(n/d)*A003602(d));

Crossrefs

Cf. A003602, A126760.

Cf. A347233, A347234, A349391, A349392, A349393, A349395, A349431, A349444, A349447 for other Dirichlet convolutions of A126760. And also A349370.

Sequence in context: A328745 A357134 A003967 * A099209 A099208 A331299

Adjacent sequences: A349387 A349388 A349389 * A349391 A349392 A349393

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved