A010803 15th powers: a(n) = n^15.

0, 1, 32768, 14348907, 1073741824, 30517578125, 470184984576, 4747561509943, 35184372088832, 205891132094649, 1000000000000000, 4177248169415651, 15407021574586368, 51185893014090757, 155568095557812224

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 (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).

Crossrefs

Cf. A013673 (zeta(15)).

Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A000584 (5th powers), A001015 (7th powers), A008455 (11th powers).

Programs

Magma

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

Mathematica

Table[n^15,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2010 *)

PARI

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

PARI

A010803(n)=n^15 \\ M. F. Hasler, Jul 03 2025

Python

A010803 = lambda n: n**15 # M. F. Hasler, Jul 03 2025

Formula

Totally multiplicative with a(p) = p^15 for prime p. Multiplicative with a(p^e) = p^(15e). - Jaroslav Krizek, Nov 01 2009

From Ilya Gutkovskiy, Feb 27 2017: (Start)

Dirichlet g.f.: zeta(s-15).

Sum_{n>=1} 1/a(n) = zeta(15) = A013673. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 16383*zeta(15)/16384. - Amiram Eldar, Oct 08 2020