A294237 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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