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

0,5

Links

Table of n, a(n) for n=0..71.

Index entries for sequences related to partitions

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.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A341142 A130006 A099609 * A120249 A058690 A290369

Adjacent sequences: A350862 A350863 A350864 * A350866 A350867 A350868

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 19 2022

Status

approved