A294146 Sum of the larger parts of the partitions of n into two parts with smaller part squarefree.

0, 1, 2, 5, 7, 12, 15, 18, 21, 29, 33, 43, 48, 60, 66, 72, 78, 84, 90, 106, 113, 131, 139, 147, 155, 176, 185, 208, 218, 243, 254, 265, 276, 304, 316, 328, 340, 371, 384, 397, 410, 444, 458, 494, 509, 547, 563, 579, 595, 611, 627, 669, 686, 703, 720, 737

Offset

1,3

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 - i) * mu(i)^2, where mu is the Möbius function (A008683).

Mathematica

Table[Sum[(n - i)*MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], SquareFreeQ[#[[2]]]&][[;; , 1]]], {n, 70}] (* Harvey P. Dale, Mar 23 2023 *)

Crossrefs

Cf. A008683, A008966, A294145.

Sequence in context: A063217 A088821 A057897 * A022758 A349744 A129232

Adjacent sequences: A294143 A294144 A294145 * A294147 A294148 A294149

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 23 2017

Status

approved