A280251 Sum of the larger parts of the partitions of 2n into two squarefree parts.

1, 5, 8, 18, 12, 34, 31, 63, 56, 88, 83, 129, 91, 138, 103, 195, 173, 303, 199, 345, 256, 442, 274, 482, 294, 525, 410, 539, 487, 668, 517, 714, 539, 913, 675, 1150, 776, 1131, 755, 1223, 783, 1406, 898, 1551, 1163, 1605, 1191, 1774, 1271, 1875, 1378, 2031, 1521, 2547

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Index entries for sequences related to partitions

Formula

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

a(n) = A280252(n) - A280250(n).

Maple

with(numtheory): A280251:=n->sum((2*n-i)*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280251(n), n=1..100);

Mathematica

Table[Total[Select[IntegerPartitions[2 n, {2}], AllTrue[#, SquareFreeQ]&][[;; , 1]]], {n, 60}] (* Harvey P. Dale, Apr 22 2023 *)

Crossrefs

Cf. A008683, A187129, A280226, A280250, A280252.

Sequence in context: A057592 A246638 A192170 * A104321 A196934 A359949

Adjacent sequences: A280248 A280249 A280250 * A280252 A280253 A280254

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 29 2016

Status

approved