1,2

For n>1 a(n) is the only solution >1 to core(x)^(n-1)=tau(x) where core(x) is the square-free 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]

F. Harary, Graph Theory, Page 209, Problem 16.11.

Harry J. Smith, Table of n, a(n) for n=1,...,12

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]

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]

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]

(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]

Sequence in context: A114977 A011822 A111179 this_sequence A058343 A111827 A045330

Adjacent sequences: A058888 A058889 A058890 this_sequence A058892 A058893 A058894

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), Jan 08 2001