A280252 Sum of the parts in the partitions of 2n into two squarefree parts.

2, 8, 12, 24, 20, 48, 42, 80, 72, 120, 110, 168, 130, 196, 150, 256, 238, 396, 266, 440, 336, 572, 368, 624, 400, 728, 540, 728, 638, 900, 682, 960, 726, 1224, 910, 1512, 1036, 1520, 1014, 1600, 1066, 1848, 1204, 2024, 1530, 2116, 1598, 2304, 1666, 2500, 1836, 2704

Offset: 1

Author

Wesley Ivan Hurt, Dec 29 2016

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A226237, A280226, A280250, A280251.

Programs

Maple

with(numtheory): A280252:=n->2*n*add(mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280252(n), n=1..100);

Mathematica

Table[2 n*Sum[MoebiusMu[i]^2 MoebiusMu[2 n - i]^2, {i, n}], {n, 80}] (* Wesley Ivan Hurt, Jan 05 2024 *)

Formula

a(n) = 2*n * A280226(n).

a(n) = A280250(n) + A280251(n).