%I #5 Dec 31 2018 13:18:31

%S 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,37,41,43,47,49,53,57,59,61,

%T 63,67,71,73,79,81,83,89,97,101,103,107,109,113,115,121,125,127,131,

%U 133,137,139,147,149,151,157,159,163,167,169,171,173,179,181,189,191

%N Odd numbers whose prime indices are all proper powers of the same number.

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

%C A proper power of n is a number n^k for some positive integer k.

%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: (), (2), (3), (4), (2,2), (5), (6), (7), (8), (4,2), (9), (3,3), (2,2,2), (10), (11), (12), (13), (14), (15), (4,4), (16), (8,2), (17), (18), (4,2,2), (19), (20), (21), (22), (2,2,2,2).

%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],And[OddQ[#],SameQ@@radbase/@primeMS[#]]&]

%Y Cf. A001597, A018819, A023894, A052410, A056239, A072720, A072721, A302593, A322900, A322901, A322902.

%K nonn

%O 1,2

%A _Gus Wiseman_, Dec 30 2018