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A327516
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Number of integer partitions of n that are empty, (1), or have at least two parts and these parts are pairwise coprime.
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53
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1, 1, 1, 2, 3, 5, 6, 9, 11, 14, 17, 22, 26, 32, 37, 42, 50, 59, 69, 80, 91, 101, 115, 133, 152, 170, 190, 210, 235, 265, 300, 334, 366, 398, 441, 484, 541, 597, 648, 703, 770, 848, 935, 1022, 1102, 1184, 1281, 1406, 1534, 1661, 1789, 1916, 2062, 2244, 2435
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OFFSET
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0,4
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COMMENTS
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The Heinz numbers of these partitions are given by A302696.
Note that the definition excludes partitions with repeated parts other than 1 (cf. A038348, A304709).
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(8) = 11 partitions:
(1) (11) (21) (31) (32) (51) (43) (53)
(111) (211) (41) (321) (52) (71)
(1111) (311) (411) (61) (431)
(2111) (3111) (511) (521)
(11111) (21111) (3211) (611)
(111111) (4111) (5111)
(31111) (32111)
(211111) (41111)
(1111111) (311111)
(2111111)
(11111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], #=={}||CoprimeQ@@#&]], {n, 0, 30}]
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CROSSREFS
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A000837 is the relatively prime instead of pairwise coprime version.
A101268 is the ordered version (with singletons).
A307719 counts these partitions of length 3.
A018783 counts partitions with a common divisor.
A328673 counts pairwise non-coprime partitions.
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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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