A010803 - OEIS

%I #26 Sep 08 2022 08:44:37

%S 0,1,32768,14348907,1073741824,30517578125,470184984576,4747561509943,

%T 35184372088832,205891132094649,1000000000000000,4177248169415651,

%U 15407021574586368,51185893014090757,155568095557812224

%N 15th powers: a(n) = n^15.

%C Totally multiplicative sequence with a(p) = p^15 for prime p. Multiplicative sequence with a(p^e) = p^(15e). - _Jaroslav Krizek_, Nov 01 2009

%H Vincenzo Librandi, <a href="/A010803/b010803.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).

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

%F Dirichlet g.f.: zeta(s-15).

%F Sum_{n>=1} 1/a(n) = zeta(15) = A013673. (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 16383*zeta(15)/16384. - _Amiram Eldar_, Oct 08 2020

%t Table[n^15,{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010 *)

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

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

%Y Cf. A013673.

%K nonn,mult,easy

%O 0,3

%A _N. J. A. Sloane_