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 A280245 #16 Feb 16 2025 08:33:38
%S A280245 1,0,2,2,1,6,1,8,6,6,14,6,18,14,18,24,23,30,35,38,46,54,55,74,72,90,
%T A280245 100,106,128,136,152,178,185,216,238,252,302,308,359,390,420,478,512,
%U A280245 564,628,668,745,810,871,974,1035,1140,1238,1336,1459,1586,1700,1868,1993,2168,2354,2512,2751,2930,3177,3418,3677,3960
%N A280245 Expansion of Product_{k>=1} (1 + x^prime(k))^2.
%C A280245 Number of partitions of n into distinct prime parts, with 2 types of each part.
%C A280245 Self-convolution of A000586. - _Ilya Gutkovskiy_, Jan 19 2018
%H A280245 Vaclav Kotesovec, <a href="/A280245/b280245.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)
%H A280245 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePartition.html">Prime Partition</a>
%H A280245 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280245 G.f.: Product_{k>=1} (1 + x^prime(k))^2.
%F A280245 log(a(n)) ~ 2*Pi*sqrt(n/(3*log(n/2))). - _Vaclav Kotesovec_, Jan 12 2021
%e A280245 a(5) = 6 because we have [5], [5'], [3, 2], [3', 2], [3, 2'], [3', 2'].
%t A280245 nmax = 67; CoefficientList[Series[Product[(1 + x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x]
%Y A280245 Cf. A000009, A000586, A000607, A022567, A070215.
%K A280245 nonn
%O A280245 0,3
%A A280245 _Ilya Gutkovskiy_, Dec 29 2016