A294232 Number of partitions of n into two parts with smaller part squarefree and larger part nonsquarefree.

0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 3, 3, 1, 2, 2, 3, 1, 3, 3, 4, 1, 3, 4, 4, 3, 5, 6, 6, 3, 5, 5, 6, 1, 5, 6, 6, 2, 5, 6, 5, 2, 5, 8, 8, 3, 6, 8, 9, 3, 7, 7, 10, 4, 7, 7, 9, 4, 8, 9, 9, 5, 9, 10, 10, 4, 10, 10, 12, 2, 10, 10, 11, 5, 11, 13, 12, 6

Offset

1,10

Links

Table of n, a(n) for n=1..80.

Index entries for sequences related to partitions

Formula

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

a(n) = A294101(n) - A294233(n). - Wesley Ivan Hurt, Jul 16 2025

Mathematica

Table[Sum[(1 - MoebiusMu[n - k]^2) MoebiusMu[k]^2, {k, Floor[n/2]}], {n, 80}]

Crossrefs

Cf. A008683, A008966, A294101, A294233.

Sequence in context: A054711 A241424 A334671 * A331254 A193738 A230494

Adjacent sequences: A294229 A294230 A294231 * A294233 A294234 A294235

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 25 2017

Status

approved