A349370 - OEIS

%I #13 Nov 21 2021 10:15:59

%S 1,2,4,3,6,8,8,4,14,12,12,12,14,16,28,5,18,28,20,18,38,24,24,16,35,28,

%T 48,24,30,56,32,6,58,36,60,42,38,40,68,24,42,76,44,36,108,48,48,20,66,

%U 70,88,42,54,96,92,32,98,60,60,84,62,64,148,7,108,116,68,54,118,120,72,56,74,76,176,60,126,136,80,30

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

%H Antti Karttunen, <a href="/A349370/b349370.txt">Table of n, a(n) for n = 1..20000</a>

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

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

%o (PARI)

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

%o A349370(n) = sumdiv(n,d,A003602(n/d)*A003602(d));

%Y Cf. A347954, A347955, A347956, A349136, A349371, A349372, A349373, A349374, A349375, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 15 2021