A294111 Sum of the smaller parts of the partitions of n into two parts with larger part prime.

0, 0, 1, 3, 2, 4, 2, 4, 6, 8, 4, 6, 8, 11, 6, 8, 10, 13, 16, 20, 24, 28, 20, 24, 28, 32, 22, 25, 28, 32, 36, 41, 46, 51, 38, 42, 46, 51, 36, 40, 44, 49, 54, 60, 66, 72, 54, 60, 66, 72, 78, 84, 90, 97, 104, 111, 118, 125, 102, 109, 116, 124, 100, 107, 114

Offset

1,4

Links

Table of n, a(n) for n=1..65.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], PrimeQ[#[[1]]]&][[All, 2]]], {n, 70}] (* Harvey P. Dale, Feb 05 2023 *)

Crossrefs

Cf. A010051, A294109.

Sequence in context: A089214 A057038 A175798 * A349322 A193295 A356275

Adjacent sequences: A294108 A294109 A294110 * A294112 A294113 A294114

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved