A245713 Sorted imperfect powers b^p with b > 0, p > 2, with multiplicity.

1, 8, 16, 27, 32, 64, 64, 81, 125, 128, 216, 243, 256, 256, 343, 512, 512, 625, 729, 729, 1000, 1024, 1024, 1296, 1331, 1728, 2048, 2187, 2197, 2401, 2744, 3125, 3375, 4096, 4096, 4096, 4096, 4913, 5832, 6561, 6561, 6859, 7776, 8000, 8192, 9261

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

Cf. A001597, A023057, A072103, A076467.

Sequence in context: A107606 A354561 A349306 * A320966 A036966 A076467

Adjacent sequences: A245710 A245711 A245712 * A245714 A245715 A245716

Keyword

nonn,easy

Author

Anatoly E. Voevudko, Jul 30 2014

Status

approved