A280250 Sum of the smaller parts of the partitions of 2n into 2 squarefree parts.

1, 3, 4, 6, 8, 14, 11, 17, 16, 32, 27, 39, 39, 58, 47, 61, 65, 93, 67, 95, 80, 130, 94, 142, 106, 203, 130, 189, 151, 232, 165, 246, 187, 311, 235, 362, 260, 389, 259, 377, 283, 442, 306, 473, 367, 511, 407, 530, 395, 625, 458, 673, 493, 801, 507, 782, 548, 842, 590, 901

Offset: 1

Author

Wesley Ivan Hurt, Dec 29 2016

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A185297, A280226, A280251, A280252.

Programs

Maple

with(numtheory): A280250:=n->sum(i*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280250(n), n=1..100);

Mathematica

Table[Total[Select[IntegerPartitions[2 n,{2}],AllTrue[#,SquareFreeQ]&][[;;,2]]],{n,60}] (* Harvey P. Dale, May 12 2025 *)

Formula

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

a(n) = A280252(n) - A280251(n).