A280316 -id:A280316 - cp's OEIS frontend

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

Wesley Ivan Hurt, Dec 31 2016

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

Cf. A008683, A280226, A280316, A280322.

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

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

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

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).

A280322 Sum of the squares of the larger parts of the partitions of 2n into two squarefree parts.

Original entry on oeis.org

1, 13, 34, 110, 74, 306, 339, 811, 804, 1340, 1437, 2469, 1725, 2840, 2245, 4953, 4511, 8663, 5975, 11191, 8568, 15588, 9696, 18380, 11064, 20397, 17314, 23105, 22379, 31134, 25387, 35486, 27603, 48487, 36645, 65610, 44926, 66801, 45749, 77825, 49037, 93390, 59942

Offset: 1

Wesley Ivan Hurt, Dec 31 2016

Index entries for sequences related to partitions

Cf. A008683, A280226, A280316.

with(numtheory): A280322:=n->add((2*n-i)^2*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280322(n), n=1..100);

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

a(n) = A280316(n) - A280320(n).

cp's OEIS Frontend

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

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