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 A331077 #12 Apr 19 2024 03:27:05
%S A331077 1,7,13,31,37,73,79,119,137,173,179,287,293,329,365,440,446,554,560,
%T A331077 668,704,740,746,986,1004,1040,1080,1188,1194,1410,1416,1542,1578,
%U A331077 1614,1650,1974,1980,2016,2052,2292,2298,2514,2520,2628,2736,2772,2778,3228,3246,3354,3390,3498,3504,3744,3780,4020,4056
%N A331077 a(n) = Sum_{k = 1..n} [d(k)*d_3(k)], where d = A000005, d_3 = A007425.
%C A331077 For background references see A330570.
%H A331077 Amiram Eldar, <a href="/A331077/b331077.txt">Table of n, a(n) for n = 1..10000</a>
%H A331077 E. C. Titchmarsh, <a href="https://doi.org/10.1093/qmath/os-13.1.129">Some problems in the analytic theory of numbers</a>, The Quarterly Journal of Mathematics, Vol. 1 (1942), pp. 129-152.
%F A331077 a(n) ~ c * n * log(n)^5 /5!, where c = Product_{p prime} ((1-1/p)^2*(1+2/p)) = 0.286747428434478734107... (Titchmarsh, 1942). - _Amiram Eldar_, Apr 19 2024
%t A331077 f[p_, e_] := (e+1)^2*(e+2)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate[Array[s, 100]] (* _Amiram Eldar_, Apr 19 2024 *)
%o A331077 (PARI) lista(nmax) = {my(s = 0); for(n = 1, nmax, s += vecprod(apply(e -> (e+1)^2*(e+2)/2, factor(n)[,2])); print1(s, ", "));} \\ _Amiram Eldar_, Apr 19 2024
%Y A331077 Cf. A000005, A007425.
%K A331077 nonn
%O A331077 1,2
%A A331077 _N. J. A. Sloane_, Jan 10 2020