OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
A proper power of n is a number n^k for some positive integer k.
EXAMPLE
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).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]);
Select[Range[100], And[OddQ[#], SameQ@@radbase/@primeMS[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 30 2018
STATUS
approved