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A343377
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Number of strict integer partitions of n with no part divisible by all the others.
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15
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1, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 8, 9, 13, 18, 21, 26, 32, 38, 47, 57, 66, 80, 95, 110, 132, 157, 181, 211, 246, 282, 327, 379, 435, 500, 570, 648, 743, 849, 963, 1094, 1241, 1404, 1592, 1799, 2025, 2282, 2568, 2882, 3239, 3634, 4066, 4554, 5094, 5686, 6346
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OFFSET
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0,8
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COMMENTS
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Alternative name: Number of strict integer partitions of n that are 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(12) = 9 partitions:
(3,2) (3,2,1) (4,3) (5,3) (5,4) (6,4) (6,5) (7,5)
(5,2) (4,3,1) (7,2) (7,3) (7,4) (5,4,3)
(5,2,1) (4,3,2) (5,3,2) (8,3) (6,4,2)
(5,3,1) (5,4,1) (9,2) (6,5,1)
(7,2,1) (5,4,2) (7,3,2)
(4,3,2,1) (6,4,1) (7,4,1)
(7,3,1) (8,3,1)
(5,3,2,1) (9,2,1)
(5,4,2,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], #=={}||UnsameQ@@#&&!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
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CROSSREFS
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The dual strict complement is A097986.
The strict complement is counted by A343347.
The case with smallest part not divisible by all the others is A343379.
The case with smallest part divisible by all the others 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.
Cf. A083710, A130689, A200745, A264401, A338470, A339562, A343338, A343342, A343345, A343346, 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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