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 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). 3
 1, 4, 9, 15, 525, 35, 1617, 2145, 5005, 4641, 586245, 1616615, 1550913, 21505, 7436429, 21489, 985982745, 3038795305, 78337, 13844919, 10393190665, 12838371, 6896776665, 7292509103495, 12023917269, 70691995, 37198413949697, 62483343, 80309179885, 98755025688454681, 138969249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..31. Eric Weisstein's World of Mathematics, Goldbach Partition Wikipedia, Goldbach's conjecture Index entries for sequences related to Goldbach conjecture Index entries for sequences related to partitions FORMULA a(n) = Product_{i=1..n} (i*(2*n-i))^(c(i)*c(2*n-i)), where c is the prime characteristic (A010051). a(n) = A362640(n) * A362641(n). EXAMPLE 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. MATHEMATICA Table[Product[(i*(2 n - i))^((PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1])), {i, n}], {n, 40}] CROSSREFS Cf. A010051, A045917, A238711, A362640 (product of the larger primes q), A362641 (product of the smaller primes p). Sequence in context: A228553 A356928 A357807 * A070447 A106548 A106546 Adjacent sequences: A337565 A337566 A337567 * A337569 A337570 A337571 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Sep 29 2020 STATUS approved

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Last modified September 13 03:07 EDT 2024. Contains 375857 sequences. (Running on oeis4.)