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).

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

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