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A319165 Perfect powers whose prime indices are not relatively prime. 5
9, 25, 27, 49, 81, 121, 125, 169, 243, 289, 343, 361, 441, 529, 625, 729, 841, 961, 1331, 1369, 1521, 1681, 1849, 2187, 2197, 2209, 2401, 2809, 3125, 3249, 3481, 3721, 3969, 4225, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7569, 7921, 8281, 9261, 9409 (list; graph; refs; listen; history; text; internal format)
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..47.

EXAMPLE

The sequence of integer partitions whose Heinz numbers are in the sequence begins: (22), (33), (222), (44), (2222), (55), (333), (66), (22222), (77), (444), (88), (4422), (99), (3333), (222222).

MATHEMATICA

Select[Range[10000], With[{t=Transpose[FactorInteger[#]]}, And[GCD@@PrimePi/@t[[1]]>1, GCD@@t[[2]]>1]]&]

CROSSREFS

Cf. A001597, A056239, A072774, A181819, A289509, A296150, A298748, A319151, A319161, A319163, A319164.

Sequence in context: A325373 A062739 A075109 * A319152 A244623 A117580

Adjacent sequences:  A319162 A319163 A319164 * A319166 A319167 A319168

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 12 2018

STATUS

approved

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Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)