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

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

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).

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 *)

Crossrefs

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

Sequence in context: A244607 A136483 A240494 * A356081 A004713 A050475

Adjacent sequences: A280247 A280248 A280249 * A280251 A280252 A280253

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 29 2016

Status

approved