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A007412 The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ].
(Formerly M0493)
16

%I M0493

%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

%N The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ].

%C Seems to be numbers n for which order of torsion subgroup t of the elliptic curve y^2=x^3-n 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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Last modified February 20 18:57 EST 2018. Contains 299381 sequences. (Running on oeis4.)