A010806 18th powers: a(n) = n^18.
0, 1, 262144, 387420489, 68719476736, 3814697265625, 101559956668416, 1628413597910449, 18014398509481984, 150094635296999121, 1000000000000000000, 5559917313492231481, 26623333280885243904
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
Crossrefs
Cf. A013676.
Programs
-
Magma
[n^18: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
-
Mathematica
Range[0, 17]^18 (* Alonso del Arte, Feb 17 2015 *)
-
PARI
for(n=0,15,print1(n^18,", ")) \\ Derek Orr, Feb 27 2017
Formula
Totally multiplicative sequence with a(p) = p^18 for prime p. Multiplicative sequence with a(p^e) = p^(18e). - Jaroslav Krizek, Nov 01 2009
From Ilya Gutkovskiy, Feb 27 2017: (Start)
Dirichlet g.f.: zeta(s-18).
Sum_{n>=1} 1/a(n) = 43867*Pi^18/38979295480125 = A013676. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 131071*zeta(18)/131072 = 5749691557*Pi^18/5109094217170944000. - Amiram Eldar, Oct 09 2020