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 A300413 #9 Jan 12 2021 10:47:49
%S A300413 1,0,2,2,2,6,4,10,10,14,20,22,32,38,48,60,74,90,112,134,164,196,236,
%T A300413 282,336,398,472,554,652,766,890,1046,1206,1408,1624,1876,2168,2486,
%U A300413 2860,3276,3744,4282,4878,5554,6316,7160,8124,9186,10388,11722,13216,14876,16732,18794,21084,23636
%N A300413 Expansion of Product_{k>=1} (1 + x^prime(k))/(1 - x^prime(k)).
%C A300413 Convolution of the sequences A000586 and A000607.
%H A300413 Vaclav Kotesovec, <a href="/A300413/b300413.txt">Table of n, a(n) for n = 0..10000</a>
%H A300413 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A300413 G.f.: Product_{k>=1} (1 + x^A000040(k))/(1 - x^A000040(k)).
%F A300413 log(a(n)) ~ Pi*sqrt(2*n/log(n/3)) * (1/3 + 2*sqrt(log(n/3) / log(2*n/3)) / 3). - _Vaclav Kotesovec_, Jan 12 2021
%t A300413 nmax = 55; CoefficientList[Series[Product[(1 + x^Prime[k])/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A300413 Cf. A000040, A000586, A000607, A015128, A080054, A103265, A280263, A280366, A300414, A300415.
%K A300413 nonn
%O A300413 0,3
%A A300413 _Ilya Gutkovskiy_, Mar 05 2018