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 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). 4
 1, 2, 3, 5, 35, 7, 77, 143, 143, 221, 3553, 4199, 5681, 391, 7429, 551, 351509, 392863, 589, 24679, 765049, 47027, 1175921, 58642669, 2318087, 55883, 95041567, 84323, 2961799, 5037203051, 78647, 367569469, 14263488419, 2257, 403723843, 22531226387, 461671607, 761740327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..38. 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_{k=1..n} (2n - k)^(c(k)*c(2n - k)), where c is the prime characteristic (A010051). a(n) = Product_{p+q = 2n, p<=q, and p,q prime} q. a(n) = A337568(n) / A362641(n). EXAMPLE 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. MATHEMATICA Table[Product[(2 n - k)^((PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1])), {k, n}], {n, 40}] CROSSREFS Cf. A010051, A045917, A337568 (product of all prime parts), A362641 (product of smaller primes p). Sequence in context: A276043 A041019 A041977 * A261130 A271387 A089213 Adjacent sequences: A362637 A362638 A362639 * A362641 A362642 A362643 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 28 2023 STATUS approved

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)