A010809 21st powers: a(n) = n^21.

0, 1, 2097152, 10460353203, 4398046511104, 476837158203125, 21936950640377856, 558545864083284007, 9223372036854775808, 109418989131512359209, 1000000000000000000000, 7400249944258160101211

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• mult
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).

Crossrefs

Cf. A293904.

Programs

Magma

[n^21: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011

Mathematica

Table[n^21, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2010 *)

PARI

a(n)=n^21 \\ Felix Fröhlich, Jul 16 2014

Formula

Completely multiplicative sequence with a(p) = p^21 for prime p. Multiplicative sequence with a(p^e) = p^(21e). - Jaroslav Krizek, Nov 01 2009

From Amiram Eldar, Oct 09 2020: (Start)

Dirichlet g.f.: zeta(s-21).

Sum_{n>=1} 1/a(n) = zeta(21) (A293904).

Sum_{n>=1} (-1)^(n+1)/a(n) = 1048575*zeta(21)/1048576. (End)