A349391 - OEIS

%I #11 Nov 21 2021 10:17:55

%S 0,1,1,2,1,4,1,3,2,5,1,7,1,6,5,4,1,7,1,9,6,7,1,10,3,8,3,11,1,16,1,5,7,

%T 9,7,12,1,10,8,13,1,20,1,13,9,11,1,13,4,18,9,15,1,10,8,16,10,13,1,27,

%U 1,14,11,6,9,24,1,17,11,32,1,17,1,16,18,19,9,28,1,17,4,17,1,34,10,18,13,19,1,27,10,21

%N Dirichlet convolution of A126760 with omega.

%H Antti Karttunen, <a href="/A349391/b349391.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A126760(n/d) * A001221(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[#] * PrimeNu[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 A349391(n) = sumdiv(n,d,A126760(n/d)*omega(d));

%Y Cf. A001221, A126760.

%Y Cf. A347233, A347234, A349390, A349392, A349393, A349395 for other Dirichlet convolutions of A126760. And also A347957.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 15 2021