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A345128
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Number of squarefree products s*t from all positive integer pairs (s,t), such that s + t = n, s <= t.
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0
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0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 2, 2, 3, 4, 3, 3, 3, 2, 4, 4, 4, 4, 4, 4, 3, 5, 4, 5, 5, 4, 6, 4, 5, 7, 6, 5, 6, 8, 5, 9, 7, 6, 7, 8, 7, 8, 7, 5, 8, 10, 7, 6, 8, 7, 10, 9, 7, 11, 10, 8, 10, 8, 8, 11, 10, 9, 10, 11, 10, 13, 13, 9, 12, 10, 10, 14, 12, 12, 12, 13, 11, 12
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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_{k=1..floor(n/2)} mu(k*(n-k))^2, where mu is the Möbius function (A008683).
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EXAMPLE
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a(13) = 3; The partitions of 13 into two positive integer parts (s,t) where s <= t are (1,12), (2,11), (3,10), (4,9), (5,8), (6,7). The corresponding products are 1*12, 2*11, 3*10, 4*9, 5*8, and 6*7; 3 of which are squarefree.
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MATHEMATICA
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Table[Sum[MoebiusMu[k (n - k)]^2, {k, Floor[n/2]}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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