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A335234
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Number of partitions of k_n into two parts (s,t) such that k_n | s*t, where k_n is the n-th nonsquarefree number (A013929).
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2
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1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 4, 1, 3, 2, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1, 5, 1, 3, 2, 1, 1, 1, 5, 1, 2, 1, 4, 1, 1, 1, 1, 6, 3, 1, 2, 1, 1, 1, 2, 4, 1, 1, 6, 1, 1, 2, 2, 3, 1, 1, 1, 4, 7, 1, 5, 1, 1, 2, 1, 3, 1, 2, 7, 1, 1, 1, 1, 2, 5, 4
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OFFSET
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1,5
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COMMENTS
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a(n) >= 1.
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LINKS
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EXAMPLE
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a(4) = 1; The 4th nonsquarefree number, A013929(4) = 12 has 6 partitions into two parts: (11,1), (10,2), (9,3), (8,4), (7,5) and (6,6) with corresponding products 11, 20, 27, 32, 35, 36. A013929(4) = 12 only divides the product 36, so a(4) = 1.
a(5) = 2; The 5th nonsquarefree number, A013929(5) = 16 has 8 partitions into two parts: (15,1), (14,2), (13,3), (12,4), (11,5), (10,6), (9,7) and (8,8) with corresponding products 15, 28, 39, 48, 55, 60, 63 and 64. A013929(5) = 16 divides two of these products, 48 and 64, so a(5) = 2.
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MATHEMATICA
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Table[If[Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[n/2]}] > 0, Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[n/2]}], {}], {n, 300}] // Flatten
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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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