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A010804 16th powers: a(n) = n^16.

%I A010804 #57 Jul 07 2025 01:04:05
%S A010804 0,1,65536,43046721,4294967296,152587890625,2821109907456,
%T A010804 33232930569601,281474976710656,1853020188851841,10000000000000000,
%U A010804 45949729863572161,184884258895036416,665416609183179841,2177953337809371136,6568408355712890625,18446744073709551616,48661191875666868481
%N A010804 16th powers: a(n) = n^16.
%C A010804 Exponent towers of the form n^(2^(2^2)). - _Paul Duckett_, Aug 30 2024
%H A010804 Vincenzo Librandi, <a href="/A010804/b010804.txt">Table of n, a(n) for n = 0..1000</a>
%H A010804 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A010804 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
%F A010804 Completely multiplicative with a(p) = p^16 for prime p. Multiplicative with a(p^e) = p^(16e). - _Jaroslav Krizek_, Nov 01 2009
%F A010804 From _Ilya Gutkovskiy_, Feb 27 2017: (Start)
%F A010804 Dirichlet g.f.: zeta(s-16).
%F A010804 Sum_{n>=1} 1/a(n) =  3617*Pi^16/325641566250 = A013674. (End)
%F A010804 a(n) = A001016(n)^2. - _Michel Marcus_, Feb 28 2018
%F A010804 Sum_{n>=1} (-1)^(n+1)/a(n) = 32767*zeta(16)/32768 = 16931177*Pi^16/1524374691840000. - _Amiram Eldar_, Oct 08 2020
%p A010804 A010804 := n -> n^16; # _M. F. Hasler_, Jul 03 2025
%t A010804 Range[0, 15]^16 (* _Alonso del Arte_, Feb 16 2015 *)
%o A010804 (Magma) [n^16: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o A010804 (Maxima) A010804(n):=n^16$
%o A010804 makelist(A010804(n),n,0,10); /* _Martin Ettl_, Nov 12 2012 */
%o A010804 (PARI) A010804(n)=n^16 \\ _Charles R Greathouse IV_, Jun 28 2015
%o A010804 (Python) A010804 = lambda n: n**16 # _M. F. Hasler_, Jul 03 2025
%Y A010804 Cf. A013674 (zeta(16)).
%Y A010804 Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A001016 (8th powers), A008456 (12th powers).
%K A010804 nonn,mult,easy
%O A010804 0,3
%A A010804 _N. J. A. Sloane_