A001017 Ninth powers: a(n) = n^9. (Formerly M5459 N2368)

0, 1, 512, 19683, 262144, 1953125, 10077696, 40353607, 134217728, 387420489, 1000000000, 2357947691, 5159780352, 10604499373, 20661046784, 38443359375, 68719476736, 118587876497, 198359290368, 322687697779, 512000000000, 794280046581, 1207269217792

Offset

0,3

Comments

A number of the form a(n) + a(n+1) + ... + a(n+k) is never prime for all n, k>=0. It could be proved by the method indicated in the comment in A256581. - Vladimir Shevelev and Peter J. C. Moses, Apr 04 2015

A generalization. Using modified Lengyel's 2007 ideas one can prove that, for every odd r>=3, every number of the form n^r + (n+1)^r + ... + (n+k)^r is nonprime. - Vladimir Shevelev, Apr 04 2015

Composition of the cubes with themselves. - Wesley Ivan Hurt, Apr 01 2016

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000 (first 1000 terms from T. D. Noe)

T. Lengyel, On divisibility of some power sums, INTEGERS, 7(2007), A41, 1-6.

K. MacMillan and J. Sondow, Divisibility of power sums and the generalized Erdős-Moser equation, arXiv:1010.2275 [math.NT], 2010-2011.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

Multiplicative with a(p^e) = p^(9e). - David W. Wilson, Aug 01 2001

Totally multiplicative sequence with a(p) = p^9 for primes p. - Jaroslav Krizek, Nov 01 2009

G.f.: x*(1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(x-1)^10. - R. J. Mathar, Jan 07 2011

a(n) = A000578(n)^3. - Wesley Ivan Hurt, Apr 01 2016

From Amiram Eldar, Oct 08 2020: (Start)

Sum_{n>=1} 1/a(n) = zeta(9) (A013667).

Sum_{n>=1} (-1)^(n+1)/a(n) = 255*zeta(9)/256. (End)

Maple

A001017:=n->n^9: seq(A001017(n), n=0..30); # Wesley Ivan Hurt, Apr 01 2016

Mathematica

Table[n^9, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
Range[0, 30]^9 (* Wesley Ivan Hurt, Apr 01 2016 *)

Prog

(PARI) vector(100, n, (n-1)^9) \\ Derek Orr, Aug 03 2014
(Magma) [n^9 : n in [0..40]]; // Wesley Ivan Hurt, Apr 01 2016

Crossrefs

Cf. A000578 (cubes), A013667, A256581.

Sequence in context: A321833 A351197 A017682 * A352055 A351607 A343289

Adjacent sequences: A001014 A001015 A001016 * A001018 A001019 A001020

Keyword

nonn,mult,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Sep 19 2000

Status

approved