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A343344
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Number of integer partitions of n that are either empty, or do not have smallest part dividing all the others, but do have greatest part divisible by all the others.
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9
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 5, 1, 6, 4, 6, 7, 15, 6, 16, 15, 20, 17, 36, 18, 43, 36, 46, 48, 72, 45, 93, 82, 103, 88, 152, 104, 179, 158, 191, 194, 285, 202, 328, 292, 373, 348, 502, 391, 576, 519, 659, 634, 864, 665
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OFFSET
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0,18
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COMMENTS
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Alternative name: Number of integer partitions of n with no part dividing all the others, but with a part divisible by all the others.
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LINKS
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EXAMPLE
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The a(18) = 1 through a(23) = 15 partitions (A..E = 10..14):
633222 C43 C332 C432 C64 E72
A522 66332 A5222 A552 F53
C322 633332 C3222 C433 I32
66322 6332222 663222 C3322 C443
633322 6333222 663322 C632
6322222 63222222 6333322 66632
63322222 C3332
C4322
663332
A52222
C32222
6333332
6632222
63332222
632222222
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], #=={}||!And@@IntegerQ/@(#/Min@@#)&&And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
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CROSSREFS
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The second condition alone gives A130689.
The first condition alone gives A338470.
The Heinz numbers of these partitions are 1 and A343339.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
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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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