cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A010809 #32 Jul 08 2025 01:46:12
%S A010809 0,1,2097152,10460353203,4398046511104,476837158203125,
%T A010809 21936950640377856,558545864083284007,9223372036854775808,
%U A010809 109418989131512359209,1000000000000000000000,7400249944258160101211
%N A010809 21st powers: a(n) = n^21.
%H A010809 Vincenzo Librandi, <a href="/A010809/b010809.txt">Table of n, a(n) for n = 0..1000</a>
%H A010809 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A010809 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
%F A010809 Completely multiplicative sequence with a(p) = p^21 for prime p. Multiplicative sequence with a(p^e) = p^(21e). - _Jaroslav Krizek_, Nov 01 2009
%F A010809 From _Amiram Eldar_, Oct 09 2020: (Start)
%F A010809 Dirichlet g.f.: zeta(s-21).
%F A010809 Sum_{n>=1} 1/a(n) = zeta(21) (A293904).
%F A010809 Sum_{n>=1} (-1)^(n+1)/a(n) = 1048575*zeta(21)/1048576. (End)
%t A010809 Table[n^21, {n, 0, 20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010 *)
%o A010809 (Magma) [n^21: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o A010809 (PARI) a(n)=n^21 \\ _Felix Fröhlich_, Jul 16 2014
%Y A010809 Cf. A293904.
%K A010809 nonn,mult,easy
%O A010809 0,3
%A A010809 _N. J. A. Sloane_