A349393 Inverse Möbius transform of A126760.

1, 2, 2, 3, 3, 4, 4, 4, 3, 6, 5, 6, 6, 8, 6, 5, 7, 6, 8, 9, 8, 10, 9, 8, 12, 12, 4, 12, 11, 12, 12, 6, 10, 14, 18, 9, 14, 16, 12, 12, 15, 16, 16, 15, 9, 18, 17, 10, 21, 24, 14, 18, 19, 8, 26, 16, 16, 22, 21, 18, 22, 24, 12, 7, 30, 20, 24, 21, 18, 36, 25, 12, 26, 28, 24, 24, 34, 24, 28, 15, 5, 30, 29, 24, 38, 32, 22

Offset

1,2

Links

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

Formula

a(n) = Sum_{d|n} A126760(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[#] &]; 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
A349393(n) = sumdiv(n, d, A126760(d));
(PARI) a(n)=my(a=valuation(n, 2), b=valuation(n, 3), c=(a+1)*(b+1)); sumdiv(n/3^b>>a, d, d\6*2+d%3)*c; \\ Charles R Greathouse IV, Nov 16 2021

Crossrefs

Cf. A347233, A347234, A349390, A349391, A349392, A349395 for other Dirichlet convolutions of A126760. And also A349371.

Sequence in context: A238701 A238134 A143489 * A341155 A341166 A274102

Adjacent sequences: A349390 A349391 A349392 * A349394 A349395 A349396

Keyword

nonn

Author

Antti Karttunen, Nov 16 2021

Status

approved