

A068601


a(n) = n^3  1.


27



0, 7, 26, 63, 124, 215, 342, 511, 728, 999, 1330, 1727, 2196, 2743, 3374, 4095, 4912, 5831, 6858, 7999, 9260, 10647, 12166, 13823, 15624, 17575, 19682, 21951, 24388, 26999, 29790, 32767, 35936, 39303, 42874, 46655, 50652, 54871, 59318, 63999, 68920
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OFFSET

1,2


COMMENTS

a(n) is the least positive integer k such that k can only contain 'n1' in exactly 2 different bases B, where 1 < B <= k.
A129294(n) = number of divisors of a(n) that are not greater than n.  Reinhard Zumkeller, Apr 09 2007
Apart from the first term, the same as A135300.  R. J. Mathar, Apr 29 2008
A058895(n)^3 + a(n)^3 + A033562(n)^3 = A185065(n)^3.  Vincenzo Librandi, Mar 13 2012
Numbers k such that for every nonnegative integer m, k^(3*m+1) + k^(3*m) is a cube.  Arkadiusz Wesolowski, Aug 10 2013


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

Partial sums of A003215, hex (or centered hexagonal) numbers: 3*n(n+1)+1.  Jonathan Vos Post, Mar 16 2006
G.f.: x^2*(72*x+x^2)/(1x)^4.  Colin Barker, Feb 12 2012
4*a(m^22*m+2) = (m^2m+1)^3 + (m^2m1)^3 + (m^23*m+3)^3 + (m^23*m+1)^3.  Bruno Berselli, Jun 23 2014
a(n) = Sum_{i=1..n1} (i+1)^3  i^3.  Wesley Ivan Hurt, Jul 23 2014


EXAMPLE

For n=6; 215 written in bases 6 and 42 is 555, 55 and (555, 55) are exactly 2 different bases.


MAPLE

A068601:=n>n^31: seq(A068601(n), n=1..50); # Wesley Ivan Hurt, Jul 23 2014


MATHEMATICA

f[n_]:=n^31; f[Range[60]] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011*)
LinearRecurrence[{4, 6, 4, 1}, {0, 7, 26, 63}, 50]] (* Vincenzo Librandi, Mar 11 2012 *)
Range[50]^3  1 (* Wesley Ivan Hurt, Jul 23 2014 *)


PROG

(PARI) a(n)=n^31
(MAGMA) [n^31: n in [1..40]]; // Vincenzo Librandi, Mar 11 2012
(GAP) List([1..45], n>n^31); # Muniru A Asiru, Oct 23 2018
(Python) for n in range(1, 50): print(n**31, end=', ') # Stefano Spezia, Nov 21 2018


CROSSREFS

Cf. A000217, A005448, A016921, A058895, A033562, A185065.
Sequence in context: A128972 A135300 A024001 * A268861 A221793 A299282
Adjacent sequences: A068598 A068599 A068600 * A068602 A068603 A068604


KEYWORD

nonn,easy


AUTHOR

Naohiro Nomoto, Mar 28 2002


STATUS

approved



