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A304711 Heinz numbers of integer partitions whose distinct parts are pairwise coprime.

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%I A304711 #4 May 17 2018 21:36:48
%S A304711 2,4,6,8,10,12,14,15,16,18,20,22,24,26,28,30,32,33,34,35,36,38,40,44,
%T A304711 45,46,48,50,51,52,54,55,56,58,60,62,64,66,68,69,70,72,74,75,76,77,80,
%U A304711 82,85,86,88,90,92,93,94,95,96,98,99,100,102,104,106,108,110
%N A304711 Heinz numbers of integer partitions whose distinct parts are pairwise coprime.
%C A304711 Two parts are coprime if they have no common divisor greater than 1. For partitions of length 1 note that (1) is coprime but (x) is not coprime for x > 1.
%C A304711 First differs from A289509 at a(24) = 44, A289509(24) = 42.
%e A304711 Sequence of all partitions whose distinct parts are pairwise coprime begins (1), (11), (21), (111), (31), (211), (41), (32), (1111), (221), (311), (51), (2111), (61), (411), (321), (11111), (52), (71), (43), (2211), (81), (3111).
%t A304711 Select[Range[200],CoprimeQ@@PrimePi/@FactorInteger[#][[All,1]]&]
%Y A304711 Cf. A000837, A007359, A018783, A051424, A056239, A078374, A101268, A289508, A289509, A298748, A300486, A302569, A302696, A302698, A302796, A302797, A304709.
%K A304711 nonn
%O A304711 1,1
%A A304711 _Gus Wiseman_, May 17 2018