A280320 Sum of the squares of the smaller parts of the partitions of 2n into two squarefree parts.

1, 5, 10, 14, 34, 66, 59, 75, 84, 220, 205, 309, 373, 600, 565, 665, 839, 1103, 959, 1191, 1176, 1860, 1416, 2060, 1664, 3653, 2194, 3505, 2891, 4974, 3563, 5534, 4371, 7551, 5845, 8874, 6742, 10409, 7061, 10145, 8037, 12414, 9030, 13327, 10849, 15319, 13473, 15960

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^2 * mu(i)^2 * mu(2n-i)^2, where mu is the Möbius function (A008683).

a(n) = A280316(n) - A280322(n).

Maple

with(numtheory): A280320:=n->add(i^2*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280320(n), n=1..100);

Mathematica

Table[Total[Select[IntegerPartitions[2 n, {2}], AllTrue[#, SquareFreeQ]&][[All, 2]]^2], {n, 50}] (* Harvey P. Dale, Jan 22 2023 *)

Prog

(PARI) a(n) = sum(i=1, n, i^2*issquarefree(i)*issquarefree(2*n-i)); \\ Michel Marcus, May 16 2019

Crossrefs

Cf. A008683, A280226, A280316, A280322.

Sequence in context: A224692 A020885 A258151 * A213365 A179123 A004470

Adjacent sequences: A280317 A280318 A280319 * A280321 A280322 A280323

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 31 2016

Status

approved