This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A349372 #12 Nov 21 2021 10:17:07
%S A349372 1,3,4,6,5,12,6,10,12,15,8,24,9,18,22,15,11,36,12,30,27,24,14,40,22,
%T A349372 27,34,36,17,66,18,21,37,33,36,72,21,36,42,50,23,81,24,48,72,42,26,60,
%U A349372 36,66,52,54,29,102,50,60,57,51,32,132,33,54,90,28,57,111,36,66,67,108,38,120,39,63,104,72,63,126,42,75
%N A349372 Dirichlet convolution of Kimberling's paraphrases (A003602) with tau (number of divisors, A000005).
%H A349372 Antti Karttunen, <a href="/A349372/b349372.txt">Table of n, a(n) for n = 1..20000</a>
%F A349372 a(n) = Sum_{d|n} A003602(n/d) * A000005(d).
%t A349372 k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, k[#] * DivisorSigma[0, n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 16 2021 *)
%o A349372 (PARI)
%o A349372 A003602(n) = (1+(n>>valuation(n,2)))/2;
%o A349372 A349372(n) = sumdiv(n,d,A003602(n/d)*numdiv(d));
%Y A349372 Cf. A000005, A003602.
%Y A349372 Cf. A347954, A347955, A347956, A349136, A349370, A349371, A349373, A349374, A349375, A349390, A349431, A349444, A349447 for Dirichlet convolutions of other sequences with A003602.
%Y A349372 Cf. also A349392.
%K A349372 nonn
%O A349372 1,2
%A A349372 _Antti Karttunen_, Nov 15 2021