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A368822
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Number of compositions of n into two non-refactorable parts.
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0
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0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 4, 5, 4, 6, 8, 8, 8, 11, 10, 9, 10, 12, 12, 15, 14, 13, 14, 17, 16, 19, 20, 19, 20, 24, 22, 23, 22, 23, 24, 27, 24, 27, 28, 27, 28, 34, 32, 31, 32, 35, 34, 37, 36, 37, 38, 41, 38, 41, 40, 41, 40, 45, 44, 43, 44, 49, 48, 47, 48, 52, 50, 53, 50, 53, 52
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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..n-1} c(k) * c(n-k), where c = A368625.
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EXAMPLE
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a(12) = 3 since there are 3 ordered ways to write 12 as the sum of two non-refactorable numbers: 5 + 7 = 6 + 6 = 7 + 5.
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MATHEMATICA
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Table[Sum[(Ceiling[k/DivisorSigma[0, k]] - Floor[k/DivisorSigma[0, k]]) (Ceiling[(n - k)/DivisorSigma[0, (n - k)]] - Floor[(n - k)/DivisorSigma[0, (n - k)]]), {k, n - 1}], {n, 100}]
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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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