

A066510


Conjectured list of positive numbers which are not of the form r^is^j, where r,s,i,j are integers with i>1, j>1.


2



6, 14, 34, 42, 58, 62, 66, 70, 78, 86, 90, 102, 110, 114, 130, 158, 178, 182, 202, 210, 230, 238, 254, 258, 266, 274, 278, 302, 306, 310, 314, 322, 326, 330, 358, 374, 378, 390, 394, 398, 402, 410, 418, 422, 426, 430, 434, 438, 446, 450, 454
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OFFSET

1,1


COMMENTS

This is a famous hard problem and the terms shown are only conjectured values.
The terms shown are not the difference of two powers below 10^19.  Don Reble.
One can immediately represent the odd numbers and the multiples of four as differences of two squares.  Don Reble.
The terms shown are not the difference of two powers below 10^27.  Mauro Fiorentini, Jan 08 2020


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Sections D9 and B19.


LINKS

Mauro Fiorentini, Table of n, a(n) for n = 1..119
Alf van der Poorten, Remarks on the sequence of 'perfect' powers


EXAMPLE

Examples showing that certain numbers are not in the sequence: 10 = 13^33^7, 22 = 7^2  3^3, 29 = 15^2  14^2, 31 = 2^5  1, 52 = 14^2  12^2, 54 = 3^4  3^3, 60 = 2^6  2^2, 68 = 10^2  2^5, 72 = 3^4  3^2, 76 = 5^3  7^2, 84 = 10^2  2^4, ...
50 = 7^2  1^3, 82 = 9^2  1^3, 226 = 15^2  1^3, 246 = 11^2  5^3, 290 = 17^2  1^3, ... [Typos corrected by Gerry Myerson, May 14 2008]


CROSSREFS

Cf. A074980, A023057.
Sequence in context: A078836 A142875 A074981 * A279730 A269717 A271097
Adjacent sequences: A066507 A066508 A066509 * A066511 A066512 A066513


KEYWORD

nonn,hard


AUTHOR

Don Reble, Oct 12 2002


STATUS

approved



