

A173341


Numbers n such that n^5 and a cube are between consecutive squares.


2



2, 23, 199, 201, 408, 575, 603, 1354, 1628, 4995, 5745, 7320, 7994, 12634, 42637, 44217, 45962, 67132, 82131, 82351, 91116, 91134, 146521, 177682, 229863, 359373, 394826, 458908, 462763, 512012, 665719, 728982, 1009965, 1156978, 1450803
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OFFSET

1,1


COMMENTS

This sequence appears to be infinite. Sequence A117594 is a subsequence. The corresponding sequence for n^7 is A173342. Are there ever more than two perfect powers between consecutive squares?


LINKS

Table of n, a(n) for n=1..35.


EXAMPLE

2 is here because 2^5=32 and 3^3=27 are between 5^2=25 and 6^2=36.
23 is here because 23^5 and 186^3 are between 2536^2 and 2537^2.
199 is here because 199^5 and 6783^3 are between 558640^2 and 558641^2.


MATHEMATICA

t={}; Do[n2=Floor[n^(5/2)]; n3=Round[n^(5/3)]; If[n2^2<n3^3<(n2+1)^2 && n2^2<n^5<(n2+1)^2 && n3^3 != n^5, AppendTo[t, n]], {n, 10^4}]; t


CROSSREFS

A097056, A117896
Sequence in context: A130547 A200846 A198851 * A118756 A133955 A062600
Adjacent sequences: A173338 A173339 A173340 * A173342 A173343 A173344


KEYWORD

nonn


AUTHOR

T. D. Noe, Feb 16 2010


STATUS

approved



