A294101 Number of partitions of n into two parts such that one is squarefree and the other is nonsquarefree.

0, 0, 0, 0, 1, 1, 1, 0, 2, 3, 3, 1, 2, 4, 4, 1, 3, 4, 6, 2, 5, 5, 7, 2, 6, 7, 7, 4, 7, 9, 9, 4, 8, 8, 10, 1, 9, 11, 11, 4, 10, 12, 10, 4, 9, 14, 14, 5, 11, 15, 17, 5, 12, 13, 19, 8, 14, 14, 18, 8, 15, 17, 17, 9, 17, 19, 19, 7, 18, 18, 22, 3, 19, 19, 21, 8

Offset

1,9

Links

Table of n, a(n) for n=1..76.

Index entries for sequences related to partitions

Formula

a(n) = floor(n/2) - Sum_{i=1..floor(n/2)} [mu(i)^2 = mu(n-i)^2], where [] is the Iverson bracket.

From Wesley Ivan Hurt, Jul 16 2025: (Start)

a(n) = A294232(n) + A294233(n).

a(n) = A262991(n) - 2*A071068(n). (End)

Mathematica

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

Crossrefs

Cf. A008683 (mu), A008966, A071068, A262868, A262869, A262991, A294100, A294232, A294233.

Sequence in context: A106589 A335490 A334290 * A051911 A106595 A181608

Adjacent sequences: A294098 A294099 A294100 * A294102 A294103 A294104

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved