A294111 Sum of the smaller parts of the partitions of n into two parts with larger part prime.

0, 0, 1, 3, 2, 4, 2, 4, 6, 8, 4, 6, 8, 11, 6, 8, 10, 13, 16, 20, 24, 28, 20, 24, 28, 32, 22, 25, 28, 32, 36, 41, 46, 51, 38, 42, 46, 51, 36, 40, 44, 49, 54, 60, 66, 72, 54, 60, 66, 72, 78, 84, 90, 97, 104, 111, 118, 125, 102, 109, 116, 124, 100, 107, 114

Offset: 1

Author

Wesley Ivan Hurt, Oct 22 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A294109.

Programs

Mathematica

Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n,{2}],PrimeQ[#[[1]]]&][[All,2]]],{n,70}] (* Harvey P. Dale, Feb 05 2023 *)

Formula

a(n) = Sum_{i=1..floor(n/2)} i * c(n - i), where c is the prime characteristic (A010051).