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 A382123 #8 Apr 06 2025 16:51:29
%S A382123 1,7,16,35,36,112,64,155,169,252,144,560,196,448,576,651,324,1183,400,
%T A382123 1260,1024,1008,576,2480,961,1372,1600,2240,900,4032,1024,2667,2304,
%U A382123 2268,2304,5915,1444,2800,3136,5580,1764,7168,1936,5040,6084,4032,2304,10416,3249,6727,5184,6860
%N A382123 a(n) = sigma(n)*sigma(2*n)/3 for n >= 1.
%C A382123 For n >= 1, 2*A329963(n) = A087943(k) for some k; this is a consequence of the prime factorization properties of the numbers listed in A329963 and A087943 (see the comments in both entries). That is, two times any term found in A329963 (numbers k such that sigma(k) is not divisible by 3) equals a term found in A087943 (numbers k such that 3 divides sigma(k)). Therefore sigma(n)*sigma(2*n) is divisible by 3 for n >= 1.
%C A382123 Equals the logarithmic derivative of A382124.
%F A382123 a(n) = A000203(n) * A062731(n) / 3.
%F A382123 Sum_{k=1..n} a(k) ~ 2*zeta(3)*n^3/3. - _Vaclav Kotesovec_, Apr 06 2025
%o A382123 (PARI) {a(n) = sigma(n)*sigma(2*n)/3}
%o A382123 for(n=1,52, print1(a(n),", "))
%Y A382123 Cf. A382124, A382125, A087943, A329963, A347108.
%Y A382123 Cf. A000203, A062731.
%K A382123 nonn
%O A382123 1,2
%A A382123 _Paul D. Hanna_, Apr 06 2025