The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001017 Ninth powers: a(n) = n^9. (Formerly M5459 N2368) 36
 0, 1, 512, 19683, 262144, 1953125, 10077696, 40353607, 134217728, 387420489, 1000000000, 2357947691, 5159780352, 10604499373, 20661046784, 38443359375, 68719476736, 118587876497, 198359290368, 322687697779, 512000000000, 794280046581, 1207269217792 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe and 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: A283340 A321833 A017682 * A050756 A179665 A056586 Adjacent sequences:  A001014 A001015 A001016 * A001018 A001019 A001020 KEYWORD nonn,mult,easy AUTHOR EXTENSIONS More terms from James A. Sellers, Sep 19 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 14:04 EST 2020. Contains 338877 sequences. (Running on oeis4.)