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).

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

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