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 A245713 Sorted imperfect powers b^p with b > 0, p > 2, with multiplicity. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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: A090081 A059172 A107606 * A320966 A036966 A076467 Adjacent sequences:  A245710 A245711 A245712 * A245714 A245715 A245716 KEYWORD nonn,easy AUTHOR Anatoly E. Voevudko, Jul 30 2014 STATUS approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)