A319163 Perfect powers whose prime multiplicities appear with relatively prime multiplicities.

4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 144, 169, 243, 256, 289, 324, 343, 361, 400, 512, 529, 576, 625, 729, 784, 841, 961, 1024, 1331, 1369, 1600, 1681, 1728, 1849, 1936, 2025, 2048, 2187, 2197, 2209, 2304, 2401, 2500, 2704, 2809, 2916, 3125

Offset

1,1

Comments

Perfect powers n such that A181819(n) is not a perfect power (i.e. belongs to A007916).

Links

Table of n, a(n) for n=1..50.

Example

The sequence of integer partitions whose Heinz numbers are in the sequence begins: (11), (111), (22), (1111), (33), (222), (11111), (44), (111111), (2222), (55), (333), (1111111), (221111), (66), (22222), (11111111), (77), (222211), (444), (88), (331111), (111111111), (99), (22111111), (3333), (222222), (441111).

Mathematica

Select[Range[1000], And[GCD@@FactorInteger[#][[All, 2]]>1, GCD@@Length/@Split[Sort[FactorInteger[#][[All, 2]]]]==1]&]

Crossrefs

Cf. A001597, A007916, A056239, A072774, A181819, A289509, A296150, A298748, A319151, A319161, A319162, A319165.

Sequence in context: A134600 A134601 A227476 * A134611 A134612 A025475

Adjacent sequences: A319160 A319161 A319162 * A319164 A319165 A319166

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved