A294109 Sum of the larger parts of the partitions of n into two parts with smaller part prime.

0, 0, 0, 2, 3, 7, 9, 11, 13, 20, 23, 26, 29, 39, 43, 47, 51, 55, 59, 63, 67, 82, 87, 92, 97, 115, 121, 127, 133, 139, 145, 151, 157, 180, 187, 194, 201, 227, 235, 243, 251, 259, 267, 275, 283, 314, 323, 332, 341, 350, 359, 368, 377, 386, 395, 404, 413, 451

Offset: 1

Author

Wesley Ivan Hurt, Oct 22 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A294111.

Programs

Mathematica

Table[Sum[(n - i) (PrimePi[i] - PrimePi[i - 1]), {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n,{2}],PrimeQ[#[[2]]]&][[All,1]]],{n,80}] (* Harvey P. Dale, Jul 08 2019 *)

Formula

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