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

1,4

Links

Table of n, a(n) for n=1..58.

Index entries for sequences related to partitions

Formula

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

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 *)

Crossrefs

Cf. A010051, A294111.

Sequence in context: A174184 A278485 A279064 * A294263 A345745 A280110

Adjacent sequences: A294106 A294107 A294108 * A294110 A294111 A294112

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved