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%I M0493 #40 Dec 17 2021 11:18:26
%S 2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,
%T 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71
%N The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3)).
%C Seems to be numbers k for which the order of the torsion subgroup t of the elliptic curve y^2 = x^3 - k is t=1. [_Artur Jasinski_, Jun 30 2010]
%C A010057(a(n)) = 0. [_Reinhard Zumkeller_, Oct 22 2011]
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 27911
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Reinhard Zumkeller, <a href="/A007412/b007412.txt">Table of n, a(n) for n = 1..10000</a>
%H A. J. dos Reis and D. M. Silberger, <a href="http://www.jstor.org/stable/2691513">Generating nonpowers by formula</a>, Math. Mag., 63 (1990), 53-55.
%H J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%H Henry W. Gould, <a href="/A003099/a003099.pdf">Letters to N. J. A. Sloane, Oct 1973 and Jan 1974</a>.
%H R. D. Nelson, <a href="http://www.jstor.org/stable/3618253">Sequences which omit powers</a>, The Mathematical Gazette, Number 461, 1988, pages 208-211.
%F a(n) = n + A048766(n + A048766(n)). [_Reinhard Zumkeller_, Oct 22 2011]
%t With[{upto=58},Complement[Range[upto],Range[Ceiling[Power[upto, (3)^-1]]]^3]] (* _Harvey P. Dale_, Nov 09 2011 *)
%t A007412Q = ! IntegerQ[#~Surd~3] &; Select[Range[57], A007412Q] (* _JungHwan Min_, Mar 27 2017 *)
%o (Haskell)
%o a007412 n = n + a048766 (n + a048766 n) -- _Reinhard Zumkeller_, Oct 22 2011
%o (PARI) lista(nn) = for (n=1, nn, if (! ispower(n, 3), print1(n, ", "))); \\ _Michel Marcus_, May 24 2015
%Y Cf. A000578 (complement), A000037 (nonsquares).
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_
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