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A322903 Odd numbers whose prime indices are all proper powers of the same number. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A349174 A349177 A323550

Adjacent sequences:  A322900 A322901 A322902 * A322904 A322905 A322906

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 30 2018

STATUS

approved

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Last modified October 5 10:54 EDT 2022. Contains 357255 sequences. (Running on oeis4.)