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
Links
Programs
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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).