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%I #21 Jan 18 2021 18:05:41
%S 1,1,1,2,3,5,6,9,11,14,17,22,26,32,37,42,50,59,69,80,91,101,115,133,
%T 152,170,190,210,235,265,300,334,366,398,441,484,541,597,648,703,770,
%U 848,935,1022,1102,1184,1281,1406,1534,1661,1789,1916,2062,2244,2435
%N Number of integer partitions of n that are empty, (1), or have at least two parts and these parts are pairwise coprime.
%C The Heinz numbers of these partitions are given by A302696.
%C Note that the definition excludes partitions with repeated parts other than 1 (cf. A038348, A304709).
%H Fausto A. C. Cariboni, <a href="/A327516/b327516.txt">Table of n, a(n) for n = 0..750</a>
%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%F For n > 1, a(n) = A051424(n) - 1. - _Gus Wiseman_, Sep 18 2020
%e The a(1) = 1 through a(8) = 11 partitions:
%e (1) (11) (21) (31) (32) (51) (43) (53)
%e (111) (211) (41) (321) (52) (71)
%e (1111) (311) (411) (61) (431)
%e (2111) (3111) (511) (521)
%e (11111) (21111) (3211) (611)
%e (111111) (4111) (5111)
%e (31111) (32111)
%e (211111) (41111)
%e (1111111) (311111)
%e (2111111)
%e (11111111)
%t Table[Length[Select[IntegerPartitions[n],#=={}||CoprimeQ@@#&]],{n,0,30}]
%Y Cf. A038348, A302569, A304709, A304711.
%Y A000837 is the relatively prime instead of pairwise coprime version.
%Y A051424 includes all singletons, with strict case A007360.
%Y A101268 is the ordered version (with singletons).
%Y A302696 ranks these partitions, with complement A335241.
%Y A305713 is the strict case.
%Y A307719 counts these partitions of length 3.
%Y A018783 counts partitions with a common divisor.
%Y A328673 counts pairwise non-coprime partitions.
%Y Cf. A087087, A220377, A326675, A333227, A333228, A335238.
%K nonn
%O 0,4
%A _Gus Wiseman_, Sep 19 2019