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 A001017 Ninth powers: a(n) = n^9. (Formerly M5459 N2368) 46
 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 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

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Last modified November 28 08:51 EST 2023. Contains 367411 sequences. (Running on oeis4.)