%I
%S 1,2,4,6,8,10,12,14,15,16,20,22,24,26,28,30,32,33,34,35,38,40,44,46,
%T 48,51,52,55,56,58,60,62,64,66,68,69,70,74,76,77,80,82,85,86,88,92,93,
%U 94,95,96,102,104,106,110,112,116,118,119,120,122,123,124,128,132
%N Numbers whose prime indices are pairwise coprime. Nonprime Heinz numbers of integer partitions with pairwise coprime parts.
%C A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair has a common divisor other than 1. A single number is not considered coprime unless it is equal to 1.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e Sequence of integer partitions with pairwise coprime parts begins: (), (1), (11), (21), (111), (31), (211), (41), (32), (1111), (311), (51), (2111), (61), (411), (321).
%e Missing from this list are: (2), (3), (4), (22), (5), (6), (7), (221), (8), (42), (9), (33), (222).
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[200],Or[#===1,CoprimeQ@@primeMS[#]]&]
%Y Cf. A000837, A000961, A001222, A005117, A007359, A051424, A275024, A289508, A289509, A298748, A302568, A302569, A302697, A302698.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 11 2018
