%I #23 Sep 08 2022 08:44:37

%S 0,1,1048576,3486784401,1099511627776,95367431640625,3656158440062976,

%T 79792266297612001,1152921504606846976,12157665459056928801,

%U 100000000000000000000,672749994932560009201,3833759992447475122176

%N 20th powers: a(n) = n^20.

%H Vincenzo Librandi, <a href="/A010808/b010808.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

%F Totally multiplicative sequence with a(p) = p^20 for prime p. Multiplicative sequence with a(p^e) = p^(20e). - _Jaroslav Krizek_, Nov 01 2009

%F From _Ilya Gutkovskiy_, Feb 27 2017: (Start)

%F Dirichlet g.f.: zeta(s-20).

%F Sum_{n>=1} 1/a(n) = 174611*Pi^20/1531329465290625 = A013678. (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 524287*zeta(20)/524288 = 91546277357*Pi^20/802857662698291200000. - _Amiram Eldar_, Oct 09 2020

%t Table[n^20, {n, 0, 20}] (* _Amiram Eldar_, Oct 09 2020 *)

%o (Magma) [n^20: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%Y Cf. A013678.

%K nonn,mult,easy

%O 0,3

%A _N. J. A. Sloane_