OFFSET
1,2
COMMENTS
No multiple terms for b=1.
This sequence strictly follows requirements of the Beal conjecture.
Less than 550 of these powers satisfy 196 Beal's conjecture equations.
LINKS
Anatoly E. Voevudko, Table of n, a(n) for n = 1..11539
American Mathematical Society, Beal Prize
Alf van der Poorten, Remarks on the sequence of 'perfect' numbers
Anatoly E. Voevudko, Description of all powers in b245713
Eric W. Weisstein, World of Mathematics, Perfect Power
Wikipedia, Beal's conjecture
MAPLE
N:= 10^5: # to get all terms <= N
L:= [1, seq(seq(b^p, p=3..floor(log[b](N))), b=2..floor(N^(1/3)))]:
sort(L); # Robert Israel, Nov 09 2015
MATHEMATICA
mx = 10000; Join[{1}, Sort@ Flatten@ Table[b^p, {b, 2, Sqrt@ mx}, {p, 3, Log[b, mx]}]] (* Robert G. Wilson v, Nov 09 2015 *)
PROG
(PARI) A245713(lim)={my(L=List(1), lim2=logint(lim, 2)); for(p=3, lim2, for(b=2, sqrtnint(lim, p), listput(L, b^p); )); listsort(L); print(L); } \\ Anatoly E. Voevudko, Sep 21 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Anatoly E. Voevudko, Jul 30 2014
STATUS
approved