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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the least positive integer k such that k can only contain 'n-1' 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*(7-2*x+x^2)/(1-x)^4. - Colin Barker, Feb 12 2012

4*a(m^2-2*m+2) = (m^2-m+1)^3 + (m^2-m-1)^3 + (m^2-3*m+3)^3 + (m^2-3*m+1)^3. - Bruno Berselli, Jun 23 2014

a(n) = Sum_{i=1..n-1} (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^3-1: seq(A068601(n), n=1..50); # Wesley Ivan Hurt, Jul 23 2014

MATHEMATICA

f[n_]:=n^3-1; 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^3-1

(MAGMA) [n^3-1: n in [1..40]]; // Vincenzo Librandi, Mar 11 2012

(GAP) List([1..45], n->n^3-1); # Muniru A Asiru, Oct 23 2018

(Python) for n in range(1, 50): print(n**3-1, 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

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)