A349392 - OEIS

%I #12 Nov 21 2021 10:18:02

%S 1,3,3,6,4,9,5,10,6,12,6,18,7,15,12,15,8,18,9,24,15,18,10,30,16,21,10,

%T 30,12,36,13,21,18,24,26,36,15,27,21,40,16,45,17,36,24,30,18,45,26,48,

%U 24,42,20,30,35,50,27,36,22,72,23,39,30,28,40,54,25,48,30,78,26,60,27,45,48,54,44,63,29,60,15,48

%N Dirichlet convolution of A126760 with tau (number of divisors function).

%H Antti Karttunen, <a href="/A349392/b349392.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A126760(n/d) * A000005(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[#] * DivisorSigma[0, 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 A349392(n) = sumdiv(n,d,A126760(n/d)*numdiv(d));

%Y Cf. A000005, A126760.

%Y Cf. A347233, A347234, A349390, A349391, A349393, A349395 for other Dirichlet convolutions of A126760. And also A349372.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 15 2021