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A322901
Numbers whose prime indices are all powers of the same number.
6
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, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
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: (), (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).
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], SameQ@@radbase/@DeleteCases[primeMS[#], 1]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 30 2018
STATUS
approved