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

Author

Wesley Ivan Hurt, Dec 29 2016

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

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

Programs

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 *)

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).