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

0, 1, 16384, 4782969, 268435456, 6103515625, 78364164096, 678223072849, 4398046511104, 22876792454961, 100000000000000, 379749833583241, 1283918464548864, 3937376385699289, 11112006825558016, 29192926025390625, 72057594037927936, 168377826559400929, 374813367582081024

Offset

0,3

Comments

Totally multiplicative sequence with a(p) = p^14 for prime p. Multiplicative sequence with a(p^e) = p^(14e). [Jaroslav Krizek, Nov 01 2009]

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

From Ilya Gutkovskiy, Feb 27 2017: (Start)

Dirichlet g.f.: zeta(s-14).

Sum_{n>=1} 1/a(n) = 2*Pi^14/18243225 = A013672. (End)

a(n) = A001015(n)^2. - Michel Marcus, Feb 28 2018

Sum_{n>=1} (-1)^(n+1)/a(n) = 8191*zeta(14)/8192 = 8191*Pi^14/74724249600. - Amiram Eldar, Oct 08 2020

Mathematica

Range[0, 20]^14 (* Harvey P. Dale, Nov 08 2011 *)

Prog

(Magma) [n^14: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
(PARI) for(n=0, 15, print1(n^14, ", ")) \\ Derek Orr, Feb 27 2017

Crossrefs

Cf. A013672, A001015 (n^7).

Sequence in context: A223967 A016903 A017692 * A236222 A269207 A016963

Adjacent sequences: A010799 A010800 A010801 * A010803 A010804 A010805

Keyword

nonn,mult,easy

Author

N. J. A. Sloane.

Status

approved