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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
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved