%I #18 Apr 16 2018 18:51:51

%S 2,6,10,12,14,15,18,20,22,24,26,28,30,33,34,35,38,40,42,44,45,46,48,

%T 50,51,52,54,55,56,58,60,62,66,68,69,70,72,74,75,76,77,78,80,82,84,85,

%U 86,88,90,92,93,94,95,96,98,99,102,104,105,106,108,110,112,114

%N Heinz numbers of aperiodic (relatively prime multiplicities) integer partitions with relatively prime parts.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e Sequence of partitions begins: (1), (21), (31), (211), (41), (32), (221), (311), (51), (2111), (61), (411), (321), (52), (71), (43), (81), (3111), (421), (511), (322), (91), (21111), (331), (72), (611), (2221), (53), (4111).

%t Select[Range[100],With[{t=Transpose[FactorInteger[#]]},And[GCD@@PrimePi/@t[[1]]===1,GCD@@t[[2]]===1]]&] (* _Gus Wiseman_, Apr 14 2018 *)

%Y Cf. A000740, A000837, A007916, A052410, A064989, A100953, A289508, A289509, A296302, A300272.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 01 2018