A350865 Sum of the larger parts in the partitions of n into two prime parts.

0, 0, 0, 0, 2, 3, 3, 5, 5, 7, 12, 0, 7, 11, 18, 13, 24, 0, 24, 17, 30, 19, 47, 0, 49, 23, 55, 0, 40, 0, 59, 29, 48, 31, 100, 0, 102, 0, 50, 37, 89, 0, 120, 41, 109, 43, 136, 0, 181, 47, 158, 0, 117, 0, 199, 53, 133, 0, 170, 0, 252, 59, 133, 61, 261, 0, 300, 0, 98, 67, 267, 0

Offset: 0

Author

Wesley Ivan Hurt, Jan 19 2022

Keywords

• nonn

Examples

			a(10) = 12; The partitions of 10 into two prime parts are (7,3) and (5,5). The sum of the larger parts of these partitions is then 7+5 = 12.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A061358, A339399, A350866, A350883 (smaller parts).

Programs

PARI

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

Formula

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