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A370809
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Greatest number of multisets that can be obtained by choosing a prime factor of each part of an integer partition of n.
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7
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1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 4, 4, 6, 4, 6, 6, 6, 6, 8, 6, 8
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OFFSET
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0,7
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LINKS
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EXAMPLE
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For the partition (10,6,3,2) there are 4 choices: {2,2,2,3}, {2,2,3,3}, {2,2,3,5}, {2,3,3,5} so a(21) >= 4.
For the partitions of 6 we have the following choices:
(6): {{2},{3}}
(51): {}
(42): {{2,2}}
(411): {}
(33): {{3,3}}
(321): {}
(3111): {}
(222): {{2,2,2}}
(2211): {}
(21111): {}
(111111): {}
So a(6) = 2.
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MATHEMATICA
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Table[Max[Length[Union[Sort /@ Tuples[If[#==1, {}, First/@FactorInteger[#]]& /@ #]]]&/@IntegerPartitions[n]], {n, 0, 30}]
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CROSSREFS
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For just all divisors (not just prime factors) we have A370808.
Cf. A000792, A048249, A063834, A239312, A319055, A339095, A355529, A355733, A367771, A368100, A370585.
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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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