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A073842 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. 1

%I

%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

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Last modified November 29 12:15 EST 2022. Contains 358424 sequences. (Running on oeis4.)