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 A330320 #26 Nov 02 2023 07:32:54
%S A330320 2,6,12,18,26,34,42,54,66,74,86,98,106,122,142,152,164,176,188,212,
%T A330320 228,236,252,276,288,304,328,340,356,372,384,408,424,440,476,494,502,
%U A330320 518,550,566,582,598,610,646,670,678,698,728,746,770,794,806,822,854,886,918,934,942,966,990,998,1022,1064,1092,1124,1140
%N A330320 a(n) = Sum_{i=1..n} tau(i)*tau(i+1), where tau(n) = A000005(n) is the number of divisors of n.
%C A330320 For background references see A330570.
%D A330320 József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 61.
%H A330320 Vincenzo Librandi, <a href="/A330320/b330320.txt">Table of n, a(n) for n = 1..5000</a>
%H A330320 A. E. Ingham, <a href="https://doi.org/10.1112/jlms/s1-2.3.202">Some asymptotic formulae in the theory of numbers</a>, Journal of the London Mathematical Society, Vol. 1, No. 3 (1927), pp. 202-208.
%H A330320 Nikolay V. Kuznetsov, <a href="https://doi.org/10.1007/BF02106872">Convolution of the Fourier coefficients of the Eisenstein-Maass series</a>, Journal of Soviet Mathematics, Vol. 29, No. 2 (1985), pp. 1131-1159.
%F A330320 a(n) ~ (1/zeta(2)) * n * log(n)^2. - _Amiram Eldar_, Mar 05 2020
%t A330320 Accumulate[a[n_]:=DivisorSum[n+1, DivisorSigma[0, n]&]; Array[a, 66]] (* _Vincenzo Librandi_, Jan 10 2020 *)
%t A330320 Accumulate[Times@@@Partition[DivisorSigma[0,Range[70]],2,1]] (* _Harvey P. Dale_, Nov 02 2023 *)
%o A330320 (PARI) a(n) = sum(i=1, n, numdiv(i*(i+1))); \\ _Michel Marcus_, Jan 11 2020
%Y A330320 Cf. A000005, A059956, A063123.
%Y A330320 Partial sums of A092517.
%K A330320 nonn
%O A330320 1,1
%A A330320 _N. J. A. Sloane_, Dec 11 2019