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%I #6 Dec 05 2013 19:55:31
%S 1,4,9,2,25,36,49,64,3,100,121,144,169,196,225,256,289,324,361,400,
%T 441,484,529,576,5,676,729,784,841,900,961,1024,1089,1156,1225,6,1369,
%U 1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,7,2500,2601,2704
%N a(1) = 1; for n>1, a(n) = the smallest positive integer root of n not included earlier, if such a root exists, otherwise the smallest power of n not included earlier, subject to a(n)<>n.
%C Conjectured to be a rearrangement of the natural numbers.
%C This is a self-inverse permutation of the positive integers, as shown by the formula. - _Franklin T. Adams-Watters_, Jul 31 2006
%F By repeatedly taking the square root, represent n in the form m^(2^k), where m is not a square and k>=0. If k is even, a(n) = m^(2^(k+1)); if k is odd, a(n) = m^(2^(k-1)). - _Franklin T. Adams-Watters_, Jul 31 2006
%Y Cf. A073843.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Aug 13 2002
%E Extended and edited by _John W. Layman_, Jun 25 2003