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A294114
Sum of the larger parts of the partitions of 2n into two parts with smaller part prime.
2
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
1,2
FORMULA
a(n) = Sum_{i=1..n} (2*n - i) * c(i), where c is the prime characteristic (A010051).
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 *)
CROSSREFS
Sequence in context: A103182 A358703 A160698 * A144707 A045373 A075431
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved