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

0, 1, 65536, 43046721, 4294967296, 152587890625, 2821109907456, 33232930569601, 281474976710656, 1853020188851841, 10000000000000000, 45949729863572161, 184884258895036416, 665416609183179841, 2177953337809371136, 6568408355712890625, 18446744073709551616, 48661191875666868481

Offset

0,3

Comments

Completely multiplicative sequence with a(p) = p^16 for prime p. Multiplicative sequence with a(p^e) = p^(16e). - Jaroslav Krizek, Nov 01 2009

Exponent towers of the form n^(2^(2^2)). - Paul Duckett, Aug 30 2024

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Formula

a(n) = n^16.

From Ilya Gutkovskiy, Feb 27 2017: (Start)

Dirichlet g.f.: zeta(s-16).

Sum_{n>=1} 1/a(n) = 3617*Pi^16/325641566250 = A013674. (End)

a(n) = A001016(n)^2. - Michel Marcus, Feb 28 2018

Sum_{n>=1} (-1)^(n+1)/a(n) = 32767*zeta(16)/32768 = 16931177*Pi^16/1524374691840000. - Amiram Eldar, Oct 08 2020

Mathematica

Range[0, 15]^16 (* Alonso del Arte, Feb 16 2015 *)

Prog

(Magma) [n^16: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
(Maxima) A010804(n):=n^16$
makelist(A010804(n), n, 0, 10); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=n^16 \\ Charles R Greathouse IV, Jun 28 2015

Crossrefs

Cf. A013674, A001016 (n^8).

Sequence in context: A016904 A017696 A211199 * A276108 A030635 A236224

Adjacent sequences: A010801 A010802 A010803 * A010805 A010806 A010807

Keyword

nonn,mult,easy

Author

N. J. A. Sloane

Status

approved