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A008456 12th powers: a(n) = n^12.

%I A008456 #48 Jul 07 2025 00:45:53
%S A008456 0,1,4096,531441,16777216,244140625,2176782336,13841287201,
%T A008456 68719476736,282429536481,1000000000000,3138428376721,8916100448256,
%U A008456 23298085122481,56693912375296,129746337890625,281474976710656,582622237229761
%N A008456 12th powers: a(n) = n^12.
%C A008456 Numbers which are square, cubic and quartic. - _Doug Bell_, Jun 03 2017
%H A008456 Vincenzo Librandi, <a href="/A008456/b008456.txt">Table of n, a(n) for n = 0..1000</a>
%H A008456 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A008456 Multiplicative with a(p^e) = p^(12*e). - _David W. Wilson_, Aug 01 2001
%F A008456 a(n) = A000290(n)^6 = A000578(n)^4 = A000583(n)^3 = A001014(n)^2. - _Doug Bell_, Jun 03 2017
%F A008456 From _Amiram Eldar_, Oct 08 2020: (Start)
%F A008456 Sum_{n>=1} 1/a(n) = zeta(12) = 691*Pi^12/638512875 (A013670).
%F A008456 Sum_{n>=1} (-1)^(n+1)/a(n) = 2047*zeta(12)/2048 = 1414477*Pi^12/1307674368000. (End)
%F A008456 a(n) = 13*a(n-1)-78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)-1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - _Wesley Ivan Hurt_, Dec 02 2021
%F A008456 Intersection of A000578 and A000583; i.e., cubes and 4th powers. - _M. F. Hasler_, Jul 03 2025
%t A008456 Range[0,30]^12 (* _Vladimir Joseph Stephan Orlovsky_, May 05 2011 *)
%o A008456 (Magma) [n^12: n in [0..30]]; // _Vincenzo Librandi_, May 06 2011
%o A008456 (PARI) A008456(n)=n^12 \\ _M. F. Hasler_, Jul 03 2025
%o A008456 (Python) A008456 = lambda n: n**12 # _M. F. Hasler_, Jul 03 2025
%Y A008456 a(n) = A123868(n) + 1.
%Y A008456 Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A001014 (6th powers), A008454 (10th powers), A008455 (11th powers), A010801 (13th powers).
%Y A008456 Cf. A013670 (zeta(12)).
%K A008456 nonn,easy,mult
%O A008456 0,3
%A A008456 _N. J. A. Sloane_