A350883 Sum of the smaller parts of the partitions of n into two prime parts.

0, 0, 0, 0, 2, 2, 3, 2, 3, 2, 8, 0, 5, 2, 10, 2, 8, 0, 12, 2, 10, 2, 19, 0, 23, 2, 23, 0, 16, 0, 31, 2, 16, 2, 36, 0, 42, 0, 26, 2, 31, 0, 48, 2, 23, 2, 48, 0, 59, 2, 42, 0, 39, 0, 71, 2, 35, 0, 62, 0, 108, 2, 53, 2, 59, 0, 96, 0, 38, 2, 83, 0, 108, 2, 91, 2, 77, 0, 127

Offset: 0

Author

Wesley Ivan Hurt, Jan 20 2022

Keywords

• nonn

Examples

			a(10) = 8; The partitions of 10 into two prime parts are (7,3) and (5,5). The sum of the smaller parts of these partitions is then 5+3 = 8.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A339399, A350865 (larger parts), A350866.

Programs

PARI

a(n) = sum(k=1, n\2, if (isprime(k) && isprime(n-k), k)); \\ Michel Marcus, Jan 21 2022

Formula

a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k) * k, where c = A010051.

a(n) = Sum_{k=floor((n-1)^2/4)+1..floor(n^2/4)} c(2k-1) * c(2k) * A339399(2k-1), where c = A350866.