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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
OFFSET
1,2
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 28 2023
STATUS
approved