A002604 a(n) = n^6 + 1.

1, 2, 65, 730, 4097, 15626, 46657, 117650, 262145, 531442, 1000001, 1771562, 2985985, 4826810, 7529537, 11390626, 16777217, 24137570, 34012225, 47045882, 64000001, 85766122, 113379905, 148035890

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Because of Fermat's little theorem, a(n) is never divisible by 7. - Altug Alkan, Apr 08 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Equals A001014 + 1. Cf. A024004, A002522.

Programs

Magma

[n^6 + 1: n in [0..50]]; // Vincenzo Librandi, May 02 2011

Mathematica

Table[n^6+1,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,2,65,730,4097,15626,46657},30] (* Harvey P. Dale, Jul 28 2021 *)

PARI

a(n)=n^6+1

Formula

G.f. (-1 + 5*x - 72*x^2 - 282*x^3 - 317*x^4 - 51*x^5 - 2*x^6) / (x - 1)^7. - R. J. Mathar, Aug 06 2012

Sum_{n>=0} 1/a(n) = 1/2 + Pi * (coth(Pi) + (sinh(Pi) + sqrt(3)*sin(sqrt(3)*Pi)) / (cosh(Pi) - cos(sqrt(3)*Pi))) / 6 = 1.5171007340332164261529... . - Vaclav Kotesovec, Feb 14 2015

Sum_{n>=0} (-1)^n/a(n) = 1/2 + Pi/(6*sinh(Pi)) + Pi * (sqrt(3)*cosh(Pi/2) * sin((sqrt(3)*Pi)/2) + cos((sqrt(3)*Pi)/2) * sinh(Pi/2)) / (3*(cosh(Pi) - cos(sqrt(3)*Pi))) = 0.514210347292695053493... . - Vaclav Kotesovec, Feb 14 2015