A010801 13th powers: a(n) = n^13.

0, 1, 8192, 1594323, 67108864, 1220703125, 13060694016, 96889010407, 549755813888, 2541865828329, 10000000000000, 34522712143931, 106993205379072, 302875106592253, 793714773254144, 1946195068359375, 4503599627370496, 9904578032905937, 20822964865671168

Offset

0,3

Comments

a(n) mod 10 = n mod 10. - Reinhard Zumkeller, Dec 06 2004

Totally multiplicative sequence with a(p) = p^13 for primes p. Multiplicative sequence with a(p^e) = p^(13*e). - Jaroslav Krizek, Nov 01 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

G.f.: x*(x^12 + 8178*x^11 + 1479726*x^10 + 45533450*x^9 + 423281535*x^8 + 1505621508*x^7 + 2275172004*x^6 + 1505621508*x^5 + 423281535*x^4 + 45533450*x^3 + 1479726*x^2 + 8178*x + 1) / (x - 1)^14. - Colin Barker, Sep 25 2014

From Amiram Eldar, Oct 08 2020: (Start)

Sum_{n>=1} 1/a(n) = zeta(13) (A013671).

Sum_{n>=1} (-1)^(n+1)/a(n) = 4095*zeta(13)/4096. (End)

Mathematica

Range[0, 30]^13 (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)

Prog

(Magma) [n^13: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
(PARI) a(n)=n^13 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000290, A000578, A000583, A000584, A013671.

Sequence in context: A305756 A195661 A017690 * A138031 A236221 A300567

Adjacent sequences: A010798 A010799 A010800 * A010802 A010803 A010804

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved