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

0,5

Links

Table of n, a(n) for n=0..78.

Index entries for sequences related to partitions

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.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A342905 A356741 A152872 * A072832 A080328 A245555

Adjacent sequences: A350880 A350881 A350882 * A350884 A350885 A350886

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 20 2022

Status

approved