A349390 - OEIS

%I #11 Nov 21 2021 10:17:49

%S 1,2,3,3,5,6,7,4,8,10,10,9,12,14,17,5,15,16,17,15,24,20,20,12,28,24,

%T 22,21,25,34,27,6,35,30,47,24,32,34,42,20,35,48,37,30,50,40,40,15,54,

%U 56,53,36,45,44,71,28,60,50,50,51,52,54,71,7,84,70,57,45,71,94,60,32,62,64,100,51,99,84,67,25,63,70,70

%N Dirichlet convolution of A126760 with Kimberling's paraphrases, A003602.

%H Antti Karttunen, <a href="/A349390/b349390.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A126760(n/d) * A003602(d).

%t f[n_] := 2 * Floor[(m = n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3])/6] + Mod[m, 3]; k[n_] := (n/2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, f[#] * k[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 16 2021 *)

%o (PARI)

%o A003602(n) = (1+(n>>valuation(n,2)))/2;

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

%o A349390(n) = sumdiv(n,d,A126760(n/d)*A003602(d));

%Y Cf. A003602, A126760.

%Y Cf. A347233, A347234, A349391, A349392, A349393, A349395, A349431, A349444, A349447 for other Dirichlet convolutions of A126760. And also A349370.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 15 2021