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 A058891 a(n) = 2^(2^(n-1) - 1). 75
 1, 2, 8, 128, 32768, 2147483648, 9223372036854775808, 170141183460469231731687303715884105728, 57896044618658097711785492504343953926634992332820282019728792003956564819968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n > 1, a(n) is the least solution > 1 to rad(x)^(n-1) = tau(x) where rad(x) = A007947(x) is the squarefree kernel of x and tau(x) = A000005(x) the number of divisors of x. - Benoit Cloitre, Apr 18 2002 [Corrected by Michel Marcus, Oct 15 2018] For n > 1, a(n) is also the total number of possible outcomes of a knockout tournament starting with 2^(n-1) players, taking account of all matches in the tournament. - Martin Griffiths, Mar 26 2009 Also, a(n+1) = 2^(2^n-1) for n >= 1 are solutions x = y of the Diophantine equation x^y * y^x = (x+y)^z in positive integers; corresponding solutions z are in A348332 (see this last sequence for more informations and links). - Bernard Schott, Oct 13 2021 For n > 2, a(n) ends with 8. - Bernard Schott, Oct 20 2021 REFERENCES F. Harary, Graph Theory, Page 209, Problem 16.11. LINKS Harry J. Smith, Table of n, a(n) for n = 1..12 FORMULA a(n) = A053287(A000079(n-1)). a(1) = 1, a(n+1) = 2*a(n)^2. a(1) = 1, a(n+1) = 2^n*a(1)*a(2)*...*a(n). - Benoit Cloitre, Sep 13 2003 a(n) = (-1/2)*((1 + sqrt(-3))^(2^n) + (1 - sqrt(-3))^(2^n)). - Artur Jasinski, Oct 11 2008 a(n) = 2*a(n-1)^2 is an example with a(1) = 1 and k = 2 of a(n) = k*a(n-1)^2; general explicit formula: a(n) = ((a(1)*k)^(2^(n-1)))/k. - Andreas Pfaffel (andreas.pfaffel(AT)gmx.at), Apr 27 2010 a(n) = A077585(n-1) + 1. - Maurizio De Leo, Feb 25 2015 a(n) = 2^A000225(n-1). - Michel Marcus, Aug 19 2020 Sum_{n>=0} 1/a(n) = A076214. - Amiram Eldar, Oct 27 2020 MAPLE a:=1: for n from 2 to 20 do a[n]:=2*a[n-1]^2 od: seq(a[n], n=1..9); # Zerinvary Lajos, Apr 16 2009 MATHEMATICA a = 1; b = -3; Table[Expand[(-1/2) ((a + Sqrt[b])^(2^n) + (a - Sqrt[b])^(2^n))], {n, 1, 10}] (* Artur Jasinski, Oct 11 2008 *) PROG (PARI) { t=1; for (n = 1, 12, write("b058891.txt", n, " ", 2^(t-1)); t*=2; ) } \\ Harry J. Smith, Jun 23 2009 CROSSREFS Cf. A000079, A000225, A053287, A076214, A077585, A348332. Sequence in context: A307124 A111179 A178173 * A274171 A184945 A058343 Adjacent sequences:  A058888 A058889 A058890 * A058892 A058893 A058894 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 08 2001 STATUS approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)