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

Author

Wesley Ivan Hurt, Oct 23 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A008966, A294146.

Programs

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 *)

Formula

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