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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

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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