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A294146
Sum of the larger parts of the partitions of n into two parts with smaller part squarefree.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 23 2017
STATUS
approved