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A294232 Number of partitions of n into two parts with smaller part squarefree and larger part nonsquarefree. 1
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 (list; graph; refs; listen; history; text; internal format)
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)} (1 - mu(n-i)^2) * mu(i)^2, where mu is the Möbius function (A008683).

MATHEMATICA

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

CROSSREFS

Cf. A008683, A008966, 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

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Last modified September 26 14:45 EDT 2021. Contains 347668 sequences. (Running on oeis4.)