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
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), 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]
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 208-211.
FORMULA
a(n) = n + n^(1/3) + O(1). - Charles R Greathouse IV, Aug 08 2024
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
(PARI) list(lim)=my(v=List(), s=sqrtnint(lim\=1, 3), k3, k13=1); for(k=1, s, k3=k13; k13=(k+1)^3; for(n=k3+1, k13-1, listput(v, n))); for(n=s^3+1, lim, listput(v, n)); Vec(v) \\ Charles R Greathouse IV, Jun 13 2024
(Python)
from sympy import integer_nthroot
def A007412(n): return n+(k:=integer_nthroot(n, 3)[0])+int(n>=(k+1)**3-k) # Chai Wah Wu, Jun 17 2024
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved