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 A337568 #22 Feb 16 2025 08:34:00
%S A337568 1,4,9,15,525,35,1617,2145,5005,4641,586245,1616615,1550913,21505,
%T A337568 7436429,21489,985982745,3038795305,78337,13844919,10393190665,
%U A337568 12838371,6896776665,7292509103495,12023917269,70691995,37198413949697,62483343,80309179885,98755025688454681,138969249
%N A337568 Product of all the parts in the Goldbach partitions (p,q) of 2n such that p + q = 2n, p <= q, and p,q prime (or 1 if no Goldbach partition of 2n exists).
%H A337568 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A337568 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A337568 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A337568 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A337568 a(n) = Product_{i=1..n} (i*(2*n-i))^(c(i)*c(2*n-i)), where c is the prime characteristic (A010051).
%F A337568 a(n) = A362640(n) * A362641(n).
%e A337568 a(9) = 5005; 2*9 = 18 has Goldbach partitions (13,5) and (11,7). The product of all the parts is 13 * 5 * 11 * 7 = 5005.
%t A337568 Table[Product[(i*(2 n - i))^((PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1])), {i, n}], {n, 40}]
%Y A337568 Cf. A010051, A045917, A238711, A362640 (product of the larger primes q), A362641 (product of the smaller primes p).
%K A337568 nonn
%O A337568 1,2
%A A337568 _Wesley Ivan Hurt_, Sep 29 2020