A319180 - OEIS

A319180

Perfect powers whose prime indices are relatively prime.

4, 8, 16, 32, 36, 64, 100, 128, 144, 196, 216, 225, 256, 324, 400, 484, 512, 576, 676, 784, 900, 1000, 1024, 1089, 1156, 1225, 1296, 1444, 1600, 1728, 1764, 1936, 2025, 2048, 2116, 2304, 2500, 2601, 2704, 2744, 2916, 3025, 3136, 3364, 3375, 3600, 3844, 4096

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OFFSET

1,1

COMMENTS

A prime index of n is a number m such that prime(m) divides n.

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

The sequence of integer partitions whose Heinz numbers are in the sequence begins: (11), (111), (1111), (11111), (2211), (111111), (3311), (1111111), (221111), (4411), (222111), (3322), (11111111), (222211), (331111), (5511), (111111111), (22111111), (6611), (441111), (332211), (333111).

MATHEMATICA

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

CROSSREFS

Cf. A001597, A056239, A072774, A289509, A298748, A319161, A319163, A319165, A319179, A319181.

Sequence in context: A061011 A359777 A181800 * A075090 A354955 A304250

Adjacent sequences: A319177 A319178 A319179 * A319181 A319182 A319183

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 12 2018

STATUS

approved