A347233 - OEIS

%I #25 Nov 19 2021 05:06:55

%S 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,

%T 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,

%U 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

%N Möbius transform of A126760.

%H Antti Karttunen, <a href="/A347233/b347233.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A347233/a347233.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Sum_{d|n} A008683(n/d) * A126760(d).

%t 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 *)

%o (PARI)

%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760

%o A347233(n) = sumdiv(n,d,moebius(n/d)*A126760(d));

%Y Cf. A008683, A126760.

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

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

%K nonn

%O 1,7

%A _Antti Karttunen_, Aug 26 2021