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 A362640 #12 Feb 16 2025 08:34:05
%S A362640 1,2,3,5,35,7,77,143,143,221,3553,4199,5681,391,7429,551,351509,
%T A362640 392863,589,24679,765049,47027,1175921,58642669,2318087,55883,
%U A362640 95041567,84323,2961799,5037203051,78647,367569469,14263488419,2257,403723843,22531226387,461671607,761740327
%N A362640 Product of the larger primes, q, in the Goldbach partitions of 2n such that p + q = 2n, p <= q, and p,q prime (or 1 if no Goldbach partition of 2n exists).
%H A362640 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A362640 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A362640 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A362640 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A362640 a(n) = Product_{k=1..n} (2n - k)^(c(k)*c(2n - k)), where c is the prime characteristic (A010051).
%F A362640 a(n) = Product_{p+q = 2n, p<=q, and p,q prime} q.
%F A362640 a(n) = A337568(n) / A362641(n).
%e A362640 a(10) = 221; 2*10 = 20 has two Goldbach partitions, namely 17+3 and 13+7. The product of the larger parts of these partitions, is 17*13 = 221.
%t A362640 Table[Product[(2 n - k)^((PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1])), {k, n}], {n, 40}]
%Y A362640 Cf. A010051, A045917, A337568 (product of all prime parts), A362641 (product of smaller primes p).
%K A362640 nonn,easy
%O A362640 1,2
%A A362640 _Wesley Ivan Hurt_, Apr 28 2023