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 A116913 #30 Dec 30 2024 02:15:42
%S A116913 1,6,13,28,36,69,71,120,130,186,177,301,248,363,378,496,426,663,533,
%T A116913 798,734,897,783,1245,961,1254,1210,1547,1248,1914,1427,2016,1806,
%U A116913 2148,1926,2821,2036,2685,2522,3270,2502,3702,2753,3801,3510,3939,3291,5053,3648
%N A116913 Inverse Moebius transform of pentagonal numbers.
%H A116913 Seiichi Manyama, <a href="/A116913/b116913.txt">Table of n, a(n) for n = 1..10000</a>
%F A116913 a(n) = Sum_{d|n} d*(3*d-1)/2.
%F A116913 G.f.: Sum_{k>=1} k*(3*k-1)/2*x^k/(1 - x^k). - _Ilya Gutkovskiy_, May 23 2017
%F A116913 From _Amiram Eldar_, Dec 29 2024: (Start)
%F A116913 a(n) = (3*sigma_2(n) - sigma(n)) / 2 = (3*A001157(n) - A000203(n)) / 2.
%F A116913 Dirichlet g.f.: zeta(s) * (3*zeta(s-2) - zeta(s-1))/2.
%F A116913 Sum_{k=1..n} a(k) ~ (zeta(3)/2) * n^3. (End)
%t A116913 Table[Sum[d*(3d - 1)/2, {d, Divisors[n]}], {n, 101}] (* _Indranil Ghosh_, May 23 2017 *)
%o A116913 (PARI) a(n) = sumdiv(n, d, d*(3*d-1)/2); \\ _Michel Marcus_, Mar 25 2015
%o A116913 (PARI) a(n) = {my(f = factor(n)); (3 * sigma(f, 2) - sigma(f)) / 2;} \\ _Amiram Eldar_, Dec 29 2024
%Y A116913 Cf. A000326 (pentagonal numbers), A000203, A002117.
%Y A116913 Inverse Moebius transforms of polygonal numbers: A007437 (k=3), A001157 (k=4), this sequence (k=5), A278945 (k=6), A278947 (k=7).
%K A116913 easy,nonn
%O A116913 1,2
%A A116913 _Jonathan Vos Post_, Mar 19 2006
%E A116913 More terms from _Michel Marcus_, Mar 25 2015