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A343380
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Number of strict integer partitions of n with no part dividing all the others but with a part divisible by all the others.
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10
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 1, 4, 0, 1, 0, 2, 0, 4, 0, 3, 1, 2, 2, 5, 0, 5, 3, 4, 1, 9, 1, 5, 2, 4, 5, 11, 1, 6, 4, 11, 3, 13, 5, 10, 4, 11, 8, 14, 3, 10, 6, 9, 3, 15, 6, 14, 10, 18, 8
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OFFSET
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0,18
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COMMENTS
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Alternative name: Number of strict integer partitions of n that are either empty or (1) have smallest part not dividing all the others and (2) have greatest part divisible by all the others.
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LINKS
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EXAMPLE
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The a(11) = 1 through a(29) = 4 partitions (empty columns indicated by dots, A..O = 10..24):
632 . . . . . A52 . C43 . C432 C64 E72 . C643 . K52 . I92
C32 F53 C6432 K54
I32 O32
C632 I632
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], #=={}||UnsameQ@@#&&!And@@IntegerQ/@(#/Min@@#)&&And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
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CROSSREFS
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The first condition alone gives A341450.
The second condition alone gives A343347.
The opposite (and dual) version is A343381.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
A167865 counts strict chains of divisors > 1 summing to n.
A339564 counts factorizations with a selected factor.
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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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