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A010805 17th powers: a(n) = n^17.

%I A010805 #35 Jul 07 2025 18:59:22
%S A010805 0,1,131072,129140163,17179869184,762939453125,16926659444736,
%T A010805 232630513987207,2251799813685248,16677181699666569,
%U A010805 100000000000000000,505447028499293771,2218611106740436992,8650415919381337933,30491346729331195904,98526125335693359375,295147905179352825856,827240261886336764177
%N A010805 17th powers: a(n) = n^17.
%H A010805 Vincenzo Librandi, <a href="/A010805/b010805.txt">Table of n, a(n) for n = 0..1000</a>
%H A010805 <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 A010805 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 A010805 From _Ilya Gutkovskiy_, Feb 27 2017: (Start)
%F A010805 Dirichlet g.f.: zeta(s-17).
%F A010805 Sum_{n>=1} 1/a(n) =  zeta(17) = A013675. (End)
%F A010805 Sum_{n>=1} (-1)^(n+1)/a(n) = 65535*zeta(17)/65536. - _Amiram Eldar_, Oct 09 2020
%p A010805 A010805 := n -> n^17; # _M. F. Hasler_, Jul 03 2025
%t A010805 Range[0,15]^17 (* _Harvey P. Dale_, Sep 14 2011 *)
%o A010805 (Magma) [n^17: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o A010805 (PARI) for(n=0,15,print1(n^17,", ")) \\ _Derek Orr_, Feb 27 2017
%o A010805 (PARI) apply( {A010805(n)=n^17}, [0..20]) \\ Defines the function and (as "proof of concept") applies it to [0..20]. - _M. F. Hasler_, Jul 03 2025
%o A010805 (Python) A010805 = lambda n: n**17 # _M. F. Hasler_, Jul 03 2025
%Y A010805 Cf. A013675 (zeta(17)).
%Y A010805 Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A001016 (8th powers), A008456 (12th powers).
%K A010805 nonn,mult,easy
%O A010805 0,3
%A A010805 _N. J. A. Sloane_