

A007412


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


16



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, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57
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OFFSET

1,1


COMMENTS

Seems to be numbers n for which order of torsion subgroup t of the elliptic curve y^2=x^3n is t=1. [Artur Jasinski, Jun 30 2010]
A010057(a(n)) = 0. [Reinhard Zumkeller, Oct 22 2011]


REFERENCES

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 27911
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 5355.
J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
Henry W. Gould, Letters to N. J. A. Sloane, Oct 1973 and Jan 1974.
R. D. Nelson, Sequences which omit powers, The Mathematical Gazette, Number 461, 1988, pages 208211.


FORMULA

a(n) = n + A048766(n + A048766(n)). [Reinhard Zumkeller, Oct 22 2011]


MATHEMATICA

With[{upto=58}, Complement[Range[upto], Range[Ceiling[Power[upto, (3)^1]]]^3]] (* Harvey P. Dale, Nov 09 2011 *)
A007412Q = ! IntegerQ[#~Surd~3] &; Select[Range[57], A007412Q] (* JungHwan Min, Mar 27 2017 *)


PROG

(Haskell)
a007412 n = n + a048766 (n + a048766 n)  Reinhard Zumkeller, Oct 22 2011
(PARI) lista(nn) = for (n=1, nn, if (! ispower(n, 3), print1(n, ", "))); \\ Michel Marcus, May 24 2015


CROSSREFS

Cf. A000578 (complement), A000037 (nonsquares).
Sequence in context: A102352 A248182 A219227 * A270420 A220218 A096432
Adjacent sequences: A007409 A007410 A007411 * A007413 A007414 A007415


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



