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A081514
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Triangle read by rows: row n = lexicographically earliest choice for n distinct divisors of A081512(n) = m whose sum is m.
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2
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1, 0, 0, 1, 2, 3, 1, 2, 3, 6, 1, 2, 3, 6, 12, 1, 2, 3, 4, 6, 8, 1, 2, 3, 4, 6, 8, 24, 1, 2, 3, 4, 5, 10, 15, 20, 1, 2, 3, 4, 6, 7, 12, 21, 28, 1, 2, 3, 4, 5, 6, 15, 20, 24, 40, 1, 2, 3, 4, 5, 6, 8, 12, 15, 24, 40, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30, 1, 2, 3, 4, 5, 6, 9, 10, 12, 18, 20, 30, 60
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OFFSET
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1,5
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COMMENTS
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A081512(n) = smallest number m which can be expressed as the sum of n of its distinct divisors, or 0 if no such number exists. (n=2 is the only time A081512(n) = 0.)
Look at all sets of n distinct divisors d_1, ..., d_n of m = A081512(n) such that d_1+...+d_n = m, and choose the lexicographically earliest solution. That is row n of the current triangle.
The value of d_n in the lexicographically earliest solution is given in A081513.
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LINKS
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EXAMPLE
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The lexicographically earliest solutions are:
[1]
[0, 0]
[1, 2, 3]
[1, 2, 3, 6]
[1, 2, 3, 6, 12]
[1, 2, 3, 4, 6, 8]
[1, 2, 3, 4, 6, 8, 24]
[1, 2, 3, 4, 5, 10, 15, 20]
[1, 2, 3, 4, 6, 7, 12, 21, 28]
[1, 2, 3, 4, 5, 6, 15, 20, 24, 40]
[1, 2, 3, 4, 5, 6, 8, 12, 15, 24, 40]
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30]
[1, 2, 3, 4, 5, 6, 9, 10, 12, 18, 20, 30, 60]
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected by Caleb M. Shor (cshor(AT)bates.edu), Sep 26 2007
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STATUS
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approved
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