A322903 - OEIS

A322903

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

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 57, 59, 61, 63, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 131, 133, 137, 139, 147, 149, 151, 157, 159, 163, 167, 169, 171, 173, 179, 181, 189, 191

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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.

LINKS

Table of n, a(n) for n=1..60.

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

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

Sequence in context: A336620 A318978 A327755 * A363691 A349174 A349177

Adjacent sequences: A322900 A322901 A322902 * A322904 A322905 A322906

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 30 2018

STATUS

approved