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A303051
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Number of partitions of n into two distinct parts (p,q) such that p, q and p+q are all squarefree.
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1
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0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 0, 3, 2, 3, 0, 4, 0, 3, 0, 4, 4, 4, 0, 0, 4, 0, 0, 5, 4, 5, 0, 6, 6, 6, 0, 7, 6, 7, 0, 8, 7, 9, 0, 0, 7, 8, 0, 0, 0, 7, 0, 10, 0, 7, 0, 10, 10, 9, 0, 11, 10, 0, 0, 11, 10, 11, 0, 12, 12, 11, 0, 13, 13, 0, 0, 14, 12, 14, 0, 0
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OFFSET
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1,7
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor((n-1)/2)} mu(n)^2 * mu(i)^2 * mu(n-i)^2, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[MoebiusMu[n]^2 MoebiusMu[i]^2 MoebiusMu[n - i]^2, {i, Floor[(n - 1)/2]}], {n, 100}]
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PROG
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(PARI) a(n) = sum(i=1, (n-1)\2, moebius(n)^2*moebius(i)^2*moebius(n-i)^2); \\ Michel Marcus, Apr 17 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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