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A305567
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Irregular triangle where T(n,k) is the number of finite sets of positive integers with least common multiple n and greatest common divisor k, where k runs over all divisors of n.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 1, 1, 1, 1, 1, 32, 7, 2, 1, 1, 1, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 8, 4, 2, 1, 1, 1, 1, 32, 2, 7, 1, 1, 1, 1, 1, 32, 7, 1, 2, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 136, 32, 4, 7, 2, 1, 1, 1, 2
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OFFSET
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1,6
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LINKS
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EXAMPLE
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Triangle begins:
1
1 1
1 1
2 1 1
1 1
7 1 1 1
1 1
4 2 1 1
2 1 1
7 1 1 1
1 1
32 7 2 1 1 1
1 1
7 1 1 1
7 1 1 1
8 4 2 1 1
1 1
32 2 7 1 1 1
1 1
32 7 1 2 1 1
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MATHEMATICA
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Table[Length[Select[Subsets[Divisors[n]], And[GCD@@#==k, LCM@@#==n]&]], {n, 30}, {k, Divisors[n]}]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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