%I #7 Dec 31 2018 13:18:17

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,31,32,34,36,37,38,40,41,42,43,44,46,47,48,49,50,52,53,54,56,57,

%U 58,59,61,62,63,64,67,68,71,72,73,74,76,79,80,81,82,83

%N Numbers whose prime indices are all powers of the same number.

%C A prime index of n is a number m such that prime(m) divides n.

%e The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). The sequence of all integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (2), (11), (3), (21), (4), (111), (22), (31), (5), (211), (6), (41), (1111), (7), (221), (8), (311), (42), (51), (9), (2111), (33), (61), (222), (411).

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All,2]]);

%t Select[Range[100],SameQ@@radbase/@DeleteCases[primeMS[#],1]&]

%Y Cf. A001597, A018819, A052409, A052410, A056239, A072720, A072721, A302242, A302593, A322900, A322902, A322903.

%K nonn

%O 1,2

%A _Gus Wiseman_, Dec 30 2018