A294145 Sum of the smaller parts of the partitions of n into two parts with larger part squarefree.

0, 1, 1, 3, 2, 4, 3, 6, 9, 12, 10, 14, 11, 15, 12, 17, 22, 28, 34, 41, 37, 44, 40, 48, 56, 64, 59, 67, 60, 68, 61, 70, 79, 89, 82, 93, 104, 116, 109, 122, 135, 149, 142, 157, 149, 163, 154, 169, 184, 199, 214, 230, 219, 235, 251, 268, 285, 303, 292, 311, 299

Offset

1,4

Links

Table of n, a(n) for n=1..61.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} i * mu(n-i)^2, where mu is the Möbius function (A008683).

Mathematica

Table[Sum[i*MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], SquareFreeQ[#[[1]]]&][[All, 2]]], {n, 70}] (* Harvey P. Dale, Dec 26 2020 *)

Crossrefs

Cf. A008683, A008966, A294146.

Sequence in context: A026923 A058708 A141731 * A024856 A147598 A023869

Adjacent sequences: A294142 A294143 A294144 * A294146 A294147 A294148

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 23 2017

Status

approved