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A349393 Inverse Möbius transform of A126760.

%I A349393 #15 Nov 21 2021 10:18:09
%S A349393 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,
%T A349393 6,10,14,18,9,14,16,12,12,15,16,16,15,9,18,17,10,21,24,14,18,19,8,26,
%U A349393 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
%N A349393 Inverse Möbius transform of A126760.
%H A349393 Antti Karttunen, <a href="/A349393/b349393.txt">Table of n, a(n) for n = 1..20000</a>
%F A349393 a(n) = Sum_{d|n} A126760(d).
%t A349393 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 *)
%o A349393 (PARI)
%o A349393 A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
%o A349393 A349393(n) = sumdiv(n,d,A126760(d));
%o A349393 (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
%Y A349393 Cf. A347233, A347234, A349390, A349391, A349392, A349395 for other Dirichlet convolutions of A126760. And also A349371.
%K A349393 nonn
%O A349393 1,2
%A A349393 _Antti Karttunen_, Nov 16 2021