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A007412 The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3)).
(Formerly M0493)
18
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, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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]
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
A. J. dos Reis and D. M. Silberger, Generating nonpowers by formula, Math. Mag., 63 (1990), 53-55.
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]
R. D. Nelson, Sequences which omit powers, The Mathematical Gazette, Number 461, 1988, pages 208-211.
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 A336592 A335275
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)