A294114 Sum of the larger parts of the partitions of 2n into two parts with smaller part prime.

0, 2, 7, 11, 20, 26, 39, 47, 55, 63, 82, 92, 115, 127, 139, 151, 180, 194, 227, 243, 259, 275, 314, 332, 350, 368, 386, 404, 451, 471, 522, 544, 566, 588, 610, 632, 691, 715, 739, 763, 828, 854, 923, 951, 979, 1007, 1082, 1112, 1142, 1172, 1202, 1232, 1315

Offset: 1

Author

Wesley Ivan Hurt, Oct 22 2017

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A294113.

Programs

Mathematica

Table[Sum[(2 n - i) (PrimePi[i] - PrimePi[i - 1]), {i, n}], {n, 80}]
Table[Total[Select[IntegerPartitions[2 n,{2}],PrimeQ[#[[2]]]&][[All,1]]],{n,60}] (* Harvey P. Dale, Apr 19 2020 *)

Formula

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