A294097 Number of partitions of 2n into two parts such that both parts are either squarefree or nonsquarefree.

1, 2, 2, 4, 2, 5, 3, 7, 5, 8, 6, 10, 6, 10, 6, 12, 9, 17, 8, 16, 9, 18, 9, 19, 10, 21, 14, 20, 15, 22, 14, 23, 14, 27, 17, 33, 18, 30, 16, 30, 16, 33, 17, 35, 23, 34, 22, 36, 22, 39, 24, 40, 25, 49, 24, 44, 25, 46, 25, 47, 25, 50, 32, 46, 31, 48, 30, 49, 30

Offset: 1

Author

Wesley Ivan Hurt, Oct 22 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008966, A294098.

Programs

Mathematica

Table[Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[2 n - k]^2], {k, n}], {n, 80}]

Formula

a(n) = Sum_{k=1..n} [A008966(i) = A008966(2n-i)], where [] is the Iverson bracket.