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A300815
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Number of 3 division {a, b, c} (a < b < c) of n where b isn't a multiple of a, c isn't a multiple of a and c isn't a multiple of b.
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2
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1, 0, 2, 0, 2, 2, 4, 2, 7, 3, 9, 8, 10, 7, 17, 11, 16, 16, 23, 17, 32, 21, 31, 30, 36, 36, 52, 36, 47, 49, 63, 50, 73, 56, 75, 77, 80, 74, 105, 87, 105, 101, 116, 102, 133, 123, 143, 136, 144, 137, 185, 148, 170, 180, 194, 187, 218, 191, 223, 219, 247, 224, 278, 237, 263, 276, 292, 283, 321, 292, 344, 326, 340, 329, 399, 361
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OFFSET
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10,3
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LINKS
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FORMULA
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a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i/j) * c((n-i-j)/i) * c((n-i-j)/j), where c(n) = ceiling(n) - floor(n). - Wesley Ivan Hurt, Apr 13 2021
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EXAMPLE
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n |
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10 | [2, 3, 5]
12 | [2, 3, 7], [3, 4, 5]
14 | [2, 5, 7], [3, 4, 7]
15 | [3, 5, 7], [4, 5, 6]
16 | [2, 3, 11], [2, 5, 9], [3, 5, 8], [4, 5, 7]
17 | [3, 4, 10], [4, 6, 7]
18 | [2, 3, 13], [2, 5, 11], [2, 7, 9], [3, 4, 11], [3, 7, 8], [4, 5, 9], [5, 6, 7]
19 | [3, 5, 11], [4, 6, 9], [5, 6, 8]
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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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