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 A268732 #36 Apr 18 2025 21:21:42
%S A268732 1,3,5,9,11,15,17,23,27,31,33,41,43,47,51,60,62,70,72,80,84,88,90,102,
%T A268732 106,110,116,124,126,134,136,148,152,156,160,176,178,182,186,198,200,
%U A268732 208,210,218,226,230,232,250,254,262,266,274,276,288,292,304,308,312,314,330
%N A268732 Sum of the numbers of divisors of gcd(x,y) with x*y <= n.
%C A268732 Partial sums of A124315.
%H A268732 Daniel Suteu, <a href="/A268732/b268732.txt">Table of n, a(n) for n = 1..10000</a>
%H A268732 Masum Billal, <a href="https://arxiv.org/abs/2206.05023">Asymptotic Result of A Generalization of A GCD-Sum</a>, arXiv:2206.05023 [math.NT], 2022.
%H A268732 Adrian W. Dudek, <a href="http://arxiv.org/abs/1602.03555">On the Success of Mishandling Euclid's Lemma</a>, arXiv:1602.03555 [math.HO], 2016. See Remark 1 p. 3.
%H A268732 Adrian W. Dudek, <a href="https://doi.org/10.4169/amer.math.monthly.123.9.924">On the Success of Mishandling Euclid's Lemma</a>, The American Mathematical Monthly, Vol. 123, No. 9 (2016), 924-927.
%H A268732 Randell Heyman, <a href="https://arxiv.org/abs/2003.13937">A summation involving the number of divisors function and the GCD function</a>, arXiv:2003.13937 [math.NT], 2020.
%F A268732 a(n) = Sum_{k=1..floor(sqrt(n))} (2*Sum_{j=1..floor(sqrt(n/k^2))} floor(n/(j*k^2)) - floor(sqrt(n/k^2))^2). - _Daniel Suteu_, Jan 08 2019
%F A268732 a(n) = n*zeta(2)*(log(n) + 2*gamma - 1 + 2*zeta'(2)/zeta(2)) + O(sqrt(n)*log(n)), where gamma is the Euler-Mascheroni constant A001620. - _Daniel Suteu_, Jan 11 2019
%F A268732 a(n) = Sum_{i=1..n} Sum_{j=1..n} floor(sqrt(n/(i*j))). - _Ridouane Oudra_, Apr 13 2025
%t A268732 Table[Total@ Flatten@ Map[Function[k, DivisorSigma[0, GCD[#, k]] & /@ Select[Range@ n, # k <= n &]], Range@ n], {n, 60}] (* _Michael De Vlieger_, Feb 12 2016 *)
%o A268732 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, numdiv(gcd(d, k/d))));
%o A268732 (PARI) a(n) = sum(k=1, sqrtint(n), 2*sum(j=1, sqrtint(n\(k*k)), n\(j*k*k))-sqrtint(n\(k*k))^2); \\ _Daniel Suteu_, Jan 08 2019
%o A268732 (PARI) a(n)=sum(k=1,n,sum(j=1,sqrt(n/k),floor(n/k/j^2))); \\ _Benoit Cloitre_, Oct 02 2022
%Y A268732 Cf. A000005, A124315.
%Y A268732 Cf. A001620, A013661, A306016.
%K A268732 nonn
%O A268732 1,2
%A A268732 _Michel Marcus_, Feb 12 2016