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 A362641 Product of the smaller primes, p, 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, 3, 15, 5, 21, 15, 35, 21, 165, 385, 273, 55, 1001, 39, 2805, 7735, 133, 561, 13585, 273, 5865, 124355, 5187, 1265, 391391, 741, 27115, 19605131, 1767, 64515, 5766215, 217, 374187, 12212915, 313131, 170085, 142635185, 63973, 902451, 13147103255, 223041, 101065, 818183948197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..45. 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} 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} p. a(n) = A337568(n) / A362640(n). EXAMPLE a(10) = 21; 2*10 = 20 has two Goldbach partitions, namely 17+3 and 13+7. The product of the smaller parts of these partitions, is 3*7 = 21. MATHEMATICA Table[Product[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), A362640 (product of the larger primes q). Sequence in context: A039793 A106243 A109203 * A039792 A076358 A208798 Adjacent sequences: A362638 A362639 A362640 * A362642 A362643 A362644 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 28 2023 STATUS approved

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Last modified August 4 13:44 EDT 2024. Contains 374923 sequences. (Running on oeis4.)