A294237 Sum of the larger parts of the partitions of n into two parts with smaller part nonsquarefree.

0, 0, 0, 0, 0, 0, 0, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 33, 36, 39, 42, 45, 48, 63, 67, 71, 75, 79, 83, 87, 91, 111, 116, 121, 126, 149, 155, 161, 167, 193, 200, 207, 214, 221, 228, 235, 242, 273, 281, 314, 323, 332, 341, 377, 387, 425, 436, 447, 458, 469

Offset

1,8

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[(n - k) (1 - MoebiusMu[k]^2), {k, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], !SquareFreeQ[#[[2]]]&][[All, 1]]], {n, 60}] (* Harvey P. Dale, Jun 20 2021 *)

Crossrefs

Cf. A008683, A008966, A294236.

Sequence in context: A299546 A039128 A214421 * A162706 A088331 A239433

Adjacent sequences: A294234 A294235 A294236 * A294238 A294239 A294240

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 25 2017

Status

approved