A294063 Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the larger part squarefree.

0, 2, 4, 12, 6, 20, 26, 46, 52, 58, 66, 96, 80, 90, 104, 148, 162, 210, 224, 276, 290, 346, 318, 382, 352, 372, 394, 416, 438, 518, 542, 566, 592, 684, 712, 810, 838, 866, 898, 1008, 960, 1076, 1112, 1234, 1270, 1306, 1344, 1476, 1514, 1454, 1494, 1636, 1676

Offset

1,2

Links

Table of n, a(n) for n=1..53.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[2*Sum[(n - i) MoebiusMu[2 n - i]^2, {i, n}], {n, 80}]
Table[Total[#[[1]]-#[[2]]&/@Select[IntegerPartitions[2n, {2}], SquareFreeQ[ #[[1]]]&]], {n, 60}] (* Harvey P. Dale, Jan 19 2021 *)

Prog

(PARI) a(n) = 2*sum(i=1, n, (n-i)*moebius(2*n-i)^2); \\ Michel Marcus, Nov 08 2017

Crossrefs

Cf. A008683, A008966, A294062.

Sequence in context: A334766 A336847 A338118 * A290096 A261892 A278225

Adjacent sequences: A294060 A294061 A294062 * A294064 A294065 A294066

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved