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 A001016 Eighth powers: a(n) = n^8. (Formerly M5426 N2357) 57
 0, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 43046721, 100000000, 214358881, 429981696, 815730721, 1475789056, 2562890625, 4294967296, 6975757441, 11019960576, 16983563041, 25600000000, 37822859361, 54875873536, 78310985281, 110075314176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Besides the first term, this sequence is the denominator of ((Pi)^8)/9450 = 1+1/256+1/6561+1/65536+1/390625+1/1679616+... - Mohammad K. Azarian, Nov 01 2011 For n > 0, a(n) is the largest number k such that k + n^4 divides k^2 + n^4. - Derek Orr, Oct 01 2014 Fourth powers of squares and squares of 4th powers. Squares composed with themselves twice. - Wesley Ivan Hurt, Apr 01 2016 REFERENCES Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968), p. 982. 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, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA Multiplicative with a(p^e) = p^(8e). - David W. Wilson, Aug 01 2001 Totally multiplicative sequence with a(p) = p^8 for primes p. - Jaroslav Krizek, Nov 01 2009 G.f.: -x*(1+x)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)/(x-1)^9. - R. J. Mathar, Jan 07 2011 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) + 40320. - Ant King, Sep 24 2013 From Wesley Ivan Hurt, Apr 01 2016: (Start) a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9) for n>8. a(n) = A000290(n)^4 = A000290(A000290(A000290(n))). a(n) = A000583(n)^2. (End) From Amiram Eldar, Oct 08 2020: (Start) Sum_{n>=1} 1/a(n) = zeta(8) = Pi^8/9450 (A013666). Sum_{n>=1} (-1)^(n+1)/a(n) = 127*zeta(8)/128 = 127*Pi^8/1209600. (End) E.g.f.: exp(x)*x*(1 + 127*x + 966*x^2 + 1701*x^3 + 1050*x^4 + 266*x^5 + 28*x^6 + x^7). - Stefano Spezia, Jul 29 2022 MAPLE A001016:=n->n^8: seq(A001016(n), n=0..50); # Wesley Ivan Hurt, Apr 01 2016 MATHEMATICA Table[n^8, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *) PROG (Maxima) A001016(n):=n^8\$ makelist(A001016(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */ (PARI) a(n)=n^8 \\ Charles R Greathouse IV, Sep 24 2015 (Magma) [n^8 : n in [0..50]]; // Wesley Ivan Hurt, Apr 01 2016 CROSSREFS Cf. A000290 (squares), A000583 (fourth powers), A013666. Sequence in context: A016900 A017680 A210840 * A352054 A351606 A343288 Adjacent sequences: A001013 A001014 A001015 * A001017 A001018 A001019 KEYWORD nonn,easy,mult AUTHOR EXTENSIONS More terms from James A. Sellers, Sep 19 2000 STATUS approved

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Last modified December 4 07:01 EST 2022. Contains 358544 sequences. (Running on oeis4.)