cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A010802 14th powers: a(n) = n^14.

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%I A010802 #38 Jul 05 2025 16:07:05
%S A010802 0,1,16384,4782969,268435456,6103515625,78364164096,678223072849,
%T A010802 4398046511104,22876792454961,100000000000000,379749833583241,
%U A010802 1283918464548864,3937376385699289,11112006825558016,29192926025390625,72057594037927936,168377826559400929,374813367582081024
%N A010802 14th powers: a(n) = n^14.
%H A010802 Vincenzo Librandi, <a href="/A010802/b010802.txt">Table of n, a(n) for n = 0..1000</a>
%H A010802 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F A010802 Totally multiplicative with a(p) = p^14 for prime p. Multiplicative with a(p^e) = p^(14e). - _Jaroslav Krizek_, Nov 01 2009
%F A010802 From _Ilya Gutkovskiy_, Feb 27 2017: (Start)
%F A010802 Dirichlet g.f.: zeta(s-14).
%F A010802 Sum_{n>=1} 1/a(n) = 2*Pi^14/18243225 = A013672. (End)
%F A010802 a(n) = A001015(n)^2. - _Michel Marcus_, Feb 28 2018
%F A010802 Sum_{n>=1} (-1)^(n+1)/a(n) = 8191*zeta(14)/8192 = 8191*Pi^14/74724249600. - _Amiram Eldar_, Oct 08 2020
%t A010802 Range[0,20]^14 (* _Harvey P. Dale_, Nov 08 2011 *)
%o A010802 (Magma) [n^14: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o A010802 (PARI) for(n=0,15,print1(n^14,", ")) \\ _Derek Orr_, Feb 27 2017
%o A010802 (PARI) A010802(n)=n^14 \\ _M. F. Hasler_, Jul 03 2025
%o A010802 (Python) A010802 = lambda n: n**14 # _M. F. Hasler_, Jul 03 2025
%Y A010802 Cf. A013672 (zeta(14)), A001015 (n^7).
%Y A010802 Cf. A000290,  (squares), A000578,  (cubes), A000583,  (4th powers), A000584,  (5th powers), A008455 (11th powers).
%K A010802 nonn,mult,easy
%O A010802 0,3
%A A010802 _N. J. A. Sloane_