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 A073570 #30 Dec 30 2024 02:15:15
%S A073570 1,6,16,41,71,147,211,371,511,791,1002,1547,1821,2596,3146,4247,4846,
%T A073570 6627,7316,9681,10852,13657,14951,19427,20546,25577,27916,34096,35961,
%U A073570 44912,46377,56607,59922,70896,74096,90278,91391,108591,113766,133421
%N A073570 G.f.: Sum_{n >= 1} x^n/(1-x^n)^5.
%C A073570 Inverse Moebius transform of pentatope numbers. - _Jonathan Vos Post_, Mar 31 2006
%H A073570 Seiichi Manyama, <a href="/A073570/b073570.txt">Table of n, a(n) for n = 1..10000</a>
%F A073570 a(n) = (1/24) * (sigma_4(n) + 6*sigma_3(n) + 11*sigma_2(n) + 6*sigma_1(n)).
%F A073570 a(n) = Sum_{d|n} (d+1)*(d+2)*(d+3)*(d+4)/24 = Sum_{d|n} C(d+3,4) = Sum_{d|n} A000332(d+3). - _Jonathan Vos Post_, Mar 31 2006. Corrected by _Joshua Zucker_, May 04 2007
%F A073570 From _Amiram Eldar_, Dec 30 2024: (Start)
%F A073570 Dirichlet g.f.: zeta(s) * (zeta(s-4) + 6*zeta(s-3) + 11*zeta(s-2) + 6*zeta(s-2)) / 24.
%F A073570 Sum_{k=1..n} a(k) ~ (zeta(5)/120) * n^5. (End)
%t A073570 Table[(DivisorSigma[4,n]+6*DivisorSigma[3,n]+11*DivisorSigma[2,n]+ 6*DivisorSigma[ 1,n])/24,{n,40}] (* _Harvey P. Dale_, Aug 08 2013 *)
%o A073570 (PARI) a(n) = sumdiv(n, d, binomial(d+3, 4)); \\ _Seiichi Manyama_, Apr 19 2021
%o A073570 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+3, 4)*x^k/(1-x^k))) \\ _Seiichi Manyama_, Apr 19 2021
%o A073570 (PARI) a(n) = my(f = factor(n)); (sigma(f, 4) + 6*sigma(f, 3) + 11*sigma(f, 2) + 6*sigma(f)) / 24; \\ _Amiram Eldar_, Dec 30 2024
%Y A073570 Cf. A000005, A000332, A007437, A013663, A059358, A101289.
%Y A073570 Cf. A000203, A001157, A001158, A001159.
%K A073570 nonn
%O A073570 1,2
%A A073570 _Vladeta Jovovic_, Aug 31 2002
%E A073570 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007