%I
%S 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 45,46,48,50,51,52,54,55,56,58,60,62,64,66,68,69,70,72,74,75,76,77,80,
%U 82,85,86,88,90,92,93,94,95,96,98,99,100,102,104,106,108,110
%N Heinz numbers of integer partitions whose distinct parts are pairwise coprime.
%C 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 First differs from A289509 at a(24) = 44, A289509(24) = 42.
%e 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 Select[Range[200],CoprimeQ@@PrimePi/@FactorInteger[#][[All,1]]&]
%Y Cf. A000837, A007359, A018783, A051424, A056239, A078374, A101268, A289508, A289509, A298748, A300486, A302569, A302696, A302698, A302796, A302797, A304709.
%K nonn
%O 1,1
%A _Gus Wiseman_, May 17 2018
