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A370808
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Greatest number of multisets that can be obtained by choosing a divisor of each part of an integer partition of n.
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31
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1, 1, 2, 2, 3, 4, 5, 6, 7, 10, 11, 14, 17, 19, 23, 29, 30, 39, 41, 51, 58, 66, 78, 82, 102, 110, 132, 144, 162, 186, 210
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OFFSET
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0,3
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LINKS
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EXAMPLE
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For the partitions of 5 we have the following choices:
(5): {{1},{5}}
(41): {{1,1},{1,2},{1,4}}
(32): {{1,1},{1,2},{1,3},{2,3}}
(311): {{1,1,1},{1,1,3}}
(221): {{1,1,1},{1,1,2},{1,2,2}}
(2111): {{1,1,1,1},{1,1,1,2}}
(11111): {{1,1,1,1,1}}
So a(5) = 4.
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MATHEMATICA
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Table[Max[Length[Union[Sort/@Tuples[Divisors/@#]]]&/@IntegerPartitions[n]], {n, 0, 30}]
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CROSSREFS
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For just prime factors we have A370809.
The version for factorizations is A370816, for just prime factors A370817.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A355733 counts choices of divisors of prime indicec.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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