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A034262 a(n) = n^3 + n. 27
0, 2, 10, 30, 68, 130, 222, 350, 520, 738, 1010, 1342, 1740, 2210, 2758, 3390, 4112, 4930, 5850, 6878, 8020, 9282, 10670, 12190, 13848, 15650, 17602, 19710, 21980, 24418, 27030, 29822, 32800, 35970, 39338, 42910, 46692, 50690, 54910 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

n such that x^3 + x + n factors over the integers. - James R. Buddenhagen, Apr 19 2005

If a(n)=X [A155977], Y=b(n) [A071253], Z=c(n) [A034262], then X^2+Y^2 = n*Z^3; e.g., if n=3, a(3)=270, b(3)=90, c(3)=30, then 270^2+90^2=3*30^3. - Vincenzo Librandi, Nov 24 2010

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = 2*A006003(n).

a(n) = A002522(n)*A001477(n). - Zerinvary Lajos, Apr 20 2008

For n>1, a(n) = floor(n^5/(n^2-1)). - Gary Detlefs, Feb 10 2010

sum_{n>=1} 1/a(n) = 0.6718659855... = gamma + Re psi(1+i) [Borwein et al., J. Math. Anal. Appl. 316 (2006) 328]. - R. J. Mathar, Jul 17 2012

a(n) = -a(-n) for all n in Z. - Michael Somos, Jul 11 2017

MAPLE

with(combinat, fibonacci):seq(fibonacci(3, i)*i, i=0..38); # Zerinvary Lajos, Mar 20 2008

with(combinat):seq(lcm(fibonacci(3, n), n), n=0..38); # Zerinvary Lajos, Apr 20 2008

MATHEMATICA

Table[(n^3+n), {n, 0, 4!}] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *)

PROG

(Haskell)

a034262 n = a000578 n + n  -- Reinhard Zumkeller, Sep 26 2014

(PARI) {a(n) = n^3 + n}; /* Michael Somos, Jul 11 2017 */

CROSSREFS

Cf. A001477, A002522.

Cf. A000290, A001477.

Cf. A071253, A155977.

Cf. A001621.

Cf. A000578.

Sequence in context: A290461 A162524 A065137 * A180499 A167214 A034827

Adjacent sequences:  A034259 A034260 A034261 * A034263 A034264 A034265

KEYWORD

nonn,easy

AUTHOR

Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 21 2000

STATUS

approved

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Last modified August 19 08:57 EDT 2017. Contains 290794 sequences.