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A058891
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2^(2^(n-1)-1).
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15
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1, 2, 8, 128, 32768, 2147483648, 9223372036854775808, 170141183460469231731687303715884105728, 57896044618658097711785492504343953926634992332820282019728792003956564819968
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For n>1 a(n) is the only solution >1 to core(x)^(n-1)=tau(x) where core(x) is the squarefree part of x and tau(x) the number of divisors of x. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 18 2002
a(n) is, for n>1, 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. [From Martin Griffiths (griffm(AT)essex.ac.uk), Mar 26 2009]
a(n) = A053287(A000079(n-1)).
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REFERENCES
| F. Harary, Graph Theory, Page 209, Problem 16.11.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,12
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FORMULA
| 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 (benoit7848c(AT)orange.fr), Sep 13 2003
a(n)=(-1/2) ((1 + Sqrt[ -3])^(2^n) + (1 - Sqrt[ -3])^(2^n)) [From Artur Jasinski (grafix(AT)csl.pl), Oct 11 2008]
recurrence:a(n) =2*a[n-1]^2, a(1)=1 . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 16 2009]
Contribution from Andreas Pfaffel (andreas.pfaffel(AT)gmx.at), Apr 27 2010: (Start)
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. (End)
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MAPLE
| a[1]:=1: for n from 2 to 20 do a[n]:=2*a[n-1]^2 od: seq(a[n], n=1..9); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 16 2009]
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MATHEMATICA
| a = 1; b = -3; Table[Expand[(-1/2) ((a + Sqrt[b])^(2^n) + (a - Sqrt[b])^(2^n))], {n, 1, 10}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 11 2008]
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PROG
| (PARI) { t=1; for (n = 1, 12, write("b058891.txt", n, " ", 2^(t-1)); t*=2; ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 23 2009]
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CROSSREFS
| Sequence in context: A011822 A111179 A178173 * A184945 A058343 A111827
Adjacent sequences: A058888 A058889 A058890 * A058892 A058893 A058894
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 08 2001
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