A010808 20th powers: a(n) = n^20.
0, 1, 1048576, 3486784401, 1099511627776, 95367431640625, 3656158440062976, 79792266297612001, 1152921504606846976, 12157665459056928801, 100000000000000000000, 672749994932560009201, 3833759992447475122176
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
Crossrefs
Cf. A013678.
Programs
-
Magma
[n^20: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
-
Mathematica
Table[n^20, {n, 0, 20}] (* Amiram Eldar, Oct 09 2020 *)
Formula
Totally multiplicative sequence with a(p) = p^20 for prime p. Multiplicative sequence with a(p^e) = p^(20e). - Jaroslav Krizek, Nov 01 2009
From Ilya Gutkovskiy, Feb 27 2017: (Start)
Dirichlet g.f.: zeta(s-20).
Sum_{n>=1} 1/a(n) = 174611*Pi^20/1531329465290625 = A013678. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 524287*zeta(20)/524288 = 91546277357*Pi^20/802857662698291200000. - Amiram Eldar, Oct 09 2020