A010805 - OEIS

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

%S 0,1,131072,129140163,17179869184,762939453125,16926659444736,

%T 232630513987207,2251799813685248,16677181699666569,

%U 100000000000000000,505447028499293771,2218611106740436992,8650415919381337933

%N 17th powers: a(n) = n^17.

%H Vincenzo Librandi, <a href="/A010805/b010805.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18, -153, 816, -3060, 8568, -18564, 31824, -43758, 48620, -43758, 31824, -18564, 8568, -3060, 816, -153, 18, -1).

%F Totally multiplicative sequence with a(p) = p^17 for prime p. Multiplicative sequence with a(p^e) = p^(17e). - _Jaroslav Krizek_, Nov 01 2009

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

%F Dirichlet g.f.: zeta(s-17).

%F Sum_{n>=1} 1/a(n) =  zeta(17) = A013675. (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 65535*zeta(17)/65536. - _Amiram Eldar_, Oct 09 2020

%t Range[0,15]^17 (* _Harvey P. Dale_, Sep 14 2011 *)

%o (Magma) [n^17: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%o (PARI) for(n=0,15,print1(n^17,", ")) \\ _Derek Orr_, Feb 27 2017

%Y Cf. A013675.

%K nonn,mult,easy

%O 0,3

%A _N. J. A. Sloane_.