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A294145
Sum of the smaller parts of the partitions of n into two parts with larger part squarefree.
2
0, 1, 1, 3, 2, 4, 3, 6, 9, 12, 10, 14, 11, 15, 12, 17, 22, 28, 34, 41, 37, 44, 40, 48, 56, 64, 59, 67, 60, 68, 61, 70, 79, 89, 82, 93, 104, 116, 109, 122, 135, 149, 142, 157, 149, 163, 154, 169, 184, 199, 214, 230, 219, 235, 251, 268, 285, 303, 292, 311, 299
OFFSET
1,4
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i * mu(n-i)^2, where mu is the Möbius function (A008683).
MATHEMATICA
Table[Sum[i*MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], SquareFreeQ[#[[1]]]&][[All, 2]]], {n, 70}] (* Harvey P. Dale, Dec 26 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 23 2017
STATUS
approved