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A294233
Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree.
1
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 3, 1, 2, 2, 3, 1, 3, 3, 3, 1, 2, 3, 3, 1, 3, 3, 4, 0, 4, 5, 5, 2, 5, 6, 5, 2, 4, 6, 6, 2, 5, 7, 8, 2, 5, 6, 9, 4, 7, 7, 9, 4, 7, 8, 8, 4, 8, 9, 9, 3, 8, 8, 10, 1, 9, 9, 10, 3, 8, 10, 9, 4, 8, 11, 11, 3, 9
OFFSET
1,18
FORMULA
a(n) = Sum_{i=1..floor(n/2)} (1 - mu(i)^2) * mu(n-i)^2, where mu is the Möbius function (A008683).
MATHEMATICA
Table[Sum[(1 - MoebiusMu[k]^2) (MoebiusMu[n - k]^2), {k, Floor[n/2]}], {n, 80}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 25 2017
STATUS
approved