A294235 - OEIS

A294235

Number of partitions of n into two parts such that the larger part is nonsquarefree.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 16

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OFFSET

1,10

LINKS

Table of n, a(n) for n=1..77.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A008683, A008966, A294234.