A347233 Möbius transform of A126760.

1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 4, 0, 0, 0, 5, 0, 6, 0, 0, 0, 7, 0, 7, 0, 0, 0, 9, 0, 10, 0, 0, 0, 8, 0, 12, 0, 0, 0, 13, 0, 14, 0, 0, 0, 15, 0, 14, 0, 0, 0, 17, 0, 14, 0, 0, 0, 19, 0, 20, 0, 0, 0, 16, 0, 22, 0, 0, 0, 23, 0, 24, 0, 0, 0, 20, 0, 26, 0, 0, 0, 27, 0, 22, 0, 0, 0, 29, 0, 24, 0, 0, 0, 24, 0, 32

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = Sum_{d|n} A008683(n/d) * 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[#] * MoebiusMu[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
A347233(n) = sumdiv(n, d, moebius(n/d)*A126760(d));

Crossrefs

Cf. A008683, A126760.

Cf. A000004, A349339 (even and odd bisection).

Cf. also A323881, A346485, A347234, A349136, A349391, A349392, A349393, A349395.

Sequence in context: A292374 A292376 A257685 * A327172 A355524 A113503

Adjacent sequences: A347230 A347231 A347232 * A347234 A347235 A347236

Keyword

nonn

Author

Antti Karttunen, Aug 26 2021

Status

approved