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

Author

N. J. A. Sloane

Keywords

• nonn
• mult
• easy

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).

Crossrefs

Cf. A013672 (zeta(14)), A001015 (n^7).

Cf. A000290, (squares), A000578, (cubes), A000583, (4th powers), A000584, (5th powers), A008455 (11th powers).

Programs

Magma

[n^14: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011

Mathematica

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

PARI

for(n=0,15,print1(n^14,", ")) \\ Derek Orr, Feb 27 2017

PARI

A010802(n)=n^14 \\ M. F. Hasler, Jul 03 2025

Python

A010802 = lambda n: n**14 # M. F. Hasler, Jul 03 2025

Formula

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

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