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 A033196 #33 Aug 04 2025 14:24:26
%S A033196 1,12,36,96,150,432,392,768,972,1800,1452,3456,2366,4704,5400,6144,
%T A033196 5202,11664,7220,14400,14112,17424,12696,27648,18750,28392,26244,
%U A033196 37632,25230,64800,30752,49152,52272,62424,58800,93312,52022,86640
%N A033196 a(n) = n^3 * Product_{p|n, p prime} (1 + 1/p).
%H A033196 T. D. Noe, <a href="/A033196/b033196.txt">Table of n, a(n) for n=1..1000</a>
%F A033196 Dirichlet g.f.: zeta(s-2)*zeta(s-3)/zeta(2*s-4).
%F A033196 a(n) = n^2 * A001615(n) = n * A000082(n).
%F A033196 Multiplicative with a(p^e) = p^e*p^(2*e-1)*(p+1). - _Vladeta Jovovic_, Nov 16 2001
%F A033196 a(n) = Sum_{d|n} mu(d)*sigma(n^3/d^2). - _Benoit Cloitre_, Feb 16 2008
%F A033196 a(n) = A001615(n^3) = A001615(n^k)/n^(k-3), with k>2. - _Enrique Pérez Herrero_, Mar 06 2012
%F A033196 Sum_{k=1..n} a(k) ~ 15*n^4 / (4*Pi^2). - _Vaclav Kotesovec_, Feb 01 2019
%F A033196 Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/((p+1)*(p^3-1))) = 1.1392293101137663761606045655621290749920977339371831842000361508083066155... - _Vaclav Kotesovec_, Sep 20 2020
%t A033196 a[n_] := n*DivisorSum[n, MoebiusMu[n/#] DivisorSigma[1, #^2]&]; Array[a, 40] (* _Jean-François Alcover_, Dec 02 2015 *)
%o A033196 (PARI) a(n)=direuler(p=2,n,(1+p^2*X)/(1-p^3*X))[n]
%o A033196 (PARI) a(n)=sumdiv(n,d,moebius(d)*sigma(n^3/d^2)) \\ _Benoit Cloitre_, Feb 16 2008
%Y A033196 Cf. A000082, A001615.
%K A033196 nonn,easy,mult
%O A033196 1,2
%A A033196 _N. J. A. Sloane_
%E A033196 Additional comments from _Michael Somos_, May 19 2000