%I
%S 1,4,9,2,25,36,49,16,3,100,121,144,169,196,225,8,289,324,361,400,441,
%T 484,529,576,5,676,81,784,841,900,961,64,1089,1156,1225,6,1369,1444,
%U 1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,7,2500,2601,2704
%N a(1) = 1; for n > 1 a(n) = smallest number of the form n^r (with r rational != 1) not included earlier.
%C The formula in terms of A052409 and A052410 implies that the sequence is a permutation of the positive integers.  _Franklin T. AdamsWatters_, Jul 26 2006
%F a(n) = n^((b  (1)^b) / b), b = gcd(b_1, ..., b_r) with prime factorization n = p_1^b_1*...*p_r^b_r.  _Sascha Kurz_, Aug 14 2002
%F If A052409(n) is odd, a(n) = A052410(n)^(A052409(n) + 1); otherwise a(n) = A052410(n)^(A052409(n)  1).  _Franklin T. AdamsWatters_, Jul 26 2006
%e a(15) = 15^2 = 225, but a(16) = 8 = 16^(3/4).
%p for n from 2 to 150 do a := ifactors(n); b := a[2][1][2]:for j from 2 to nops(a[2]) do b := gcd(b,a[2][j][2]); od; bb := floor(evalf(n^(1/b))); if(b mod 2=1) then c[n] := bb^(b+1) else c[n] := bb^(b1); fi; od:c[1]=1:seq(c[j],j=1..150);
%Y Cf. A073842.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Aug 13 2002
%E More terms from _Sascha Kurz_, Aug 14 2002
