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A343341
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Number of integer partitions of n with no part divisible by all the others.
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20
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1, 0, 0, 0, 0, 1, 1, 4, 6, 11, 16, 28, 36, 58, 79, 111, 149, 209, 270, 368, 472, 618, 793, 1030, 1292, 1653, 2073, 2608, 3241, 4051, 4982, 6176, 7566, 9285, 11320, 13805, 16709, 20275, 24454, 29477, 35380, 42472, 50741, 60648, 72199, 85887, 101906, 120816
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OFFSET
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0,8
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COMMENTS
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Alternative name: Number of integer partitions of n that are either empty, or have greatest part not divisible by all the others.
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LINKS
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EXAMPLE
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The a(5) = 1 through a(10) = 16 partitions:
(32) (321) (43) (53) (54) (64)
(52) (332) (72) (73)
(322) (431) (432) (433)
(3211) (521) (522) (532)
(3221) (531) (541)
(32111) (3222) (721)
(3321) (3322)
(4311) (4321)
(5211) (5221)
(32211) (5311)
(321111) (32221)
(33211)
(43111)
(52111)
(322111)
(3211111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], #=={}||!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
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CROSSREFS
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The complement is counted by A130689.
The Heinz numbers of these partitions are A343337.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
Cf. A066186, A083710, A083711, A097986, A098965, A341450, A343342, A343345, A343346, A343381, A343382.
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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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