A294096 Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime and smaller part squarefree.

0, 0, 1, 2, 1, 4, 3, 8, 5, 4, 0, 12, 10, 20, 11, 16, 5, 28, 22, 38, 18, 28, 14, 48, 34, 32, 7, 24, 26, 56, 30, 64, 47, 68, 23, 60, 34, 68, 54, 58, 21, 112, 85, 144, 59, 104, 62, 168, 82, 124, 61, 110, 83, 180, 81, 124, 71, 152, 62, 202, 91, 192, 132, 224, 74

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} (n - 2i) * A008966(i) * A010051(n - i).

Mathematica

Table[Sum[(n - 2 i) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 80}]
Table[Total[#[[1]]-#[[2]]&/@Select[IntegerPartitions[n, {2}], PrimeQ[#[[1]]]&&SquareFreeQ[ #[[2]]]&]], {n, 70}] (* Harvey P. Dale, Jun 08 2024 *)

Crossrefs

Cf. A010051, A008966, A294095.

Sequence in context: A179206 A331740 A074987 * A128280 A182177 A281878

Adjacent sequences: A294093 A294094 A294095 * A294097 A294098 A294099

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved