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A010806 18th powers: a(n) = n^18. 6

%I #29 Sep 08 2022 08:44:37

%S 0,1,262144,387420489,68719476736,3814697265625,101559956668416,

%T 1628413597910449,18014398509481984,150094635296999121,

%U 1000000000000000000,5559917313492231481,26623333280885243904

%N 18th powers: a(n) = n^18.

%H Vincenzo Librandi, <a href="/A010806/b010806.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).

%F Totally multiplicative sequence with a(p) = p^18 for prime p. Multiplicative sequence with a(p^e) = p^(18e). - _Jaroslav Krizek_, Nov 01 2009

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

%F Dirichlet g.f.: zeta(s-18).

%F Sum_{n>=1} 1/a(n) = 43867*Pi^18/38979295480125 = A013676. (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 131071*zeta(18)/131072 = 5749691557*Pi^18/5109094217170944000. - _Amiram Eldar_, Oct 09 2020

%t Range[0, 17]^18 (* _Alonso del Arte_, Feb 17 2015 *)

%o (Magma) [n^18: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%o (PARI) for(n=0,15,print1(n^18,", ")) \\ _Derek Orr_, Feb 27 2017

%Y Cf. A013676.

%K nonn,mult,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)