A349375 - OEIS

%I #11 Nov 21 2021 10:17:35

%S 1,0,1,1,2,0,3,0,4,0,5,1,6,0,4,1,8,0,9,2,6,0,11,0,11,0,10,3,14,0,15,0,

%T 10,0,12,4,18,0,12,0,20,0,21,5,14,0,23,1,22,0,16,6,26,0,20,0,18,0,29,

%U 4,30,0,21,1,24,0,33,8,22,0,35,0,36,0,21,9,30,0,39,2,31,0,41,6,32,0,28,0,44,0,36,11,30,0,36

%N Dirichlet convolution of Kimberling's paraphrases (A003602) with Liouville's lambda.

%H Antti Karttunen, <a href="/A349375/b349375.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A003602(n/d) * A008836(d).

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

%o (PARI)

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

%o A008836(n) = ((-1)^bigomega(n));

%o A349375(n) = sumdiv(n,d,A003602(n/d)*A008836(d));

%Y Cf. A003602, A008836.

%Y Cf. A347954, A347955, A347956, A349136, A349370, A349371, A349372, A349373, A349374, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

%Y Cf. also A349395.

%K nonn

%O 1,5

%A _Antti Karttunen_, Nov 15 2021