

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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



KEYWORD

nonn,hard


AUTHOR



STATUS

approved



