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%I #18 May 04 2018 22:42:51
%S 1,2,1,3,4,5,1,2,6,7,8,9,10,11,1,12,13,14,15,16,17,18,19,3,20,2,21,22,
%T 23,24,1,25,26,27,4,28,29,30,31,32,33,34,35,36,37,38,39,5,40,41,42,43,
%U 44,45,46,47,48,49,50,51,52,53,1,54,55,56,57,58,59,60
%N Position in the sequence of numbers that are not perfect powers (A007916) of the smallest positive integer x such that for some positive integer y we have n = x^y (A052410).
%C Every pair p of positive integers is of the form p = (a(n), A052409(n)) for exactly one n.
%F For n>1 we have a(n) = A278028(n,1).
%e a(27)=2 because the smallest root of 27 is 3, and 3 is the 2nd entry of A007916.
%e a(25)=3 because the smallest root of 25 is 5, and 5 is the 3rd entry of A007916.
%t nn=100;
%t q=Table[Power[n,1/GCD@@FactorInteger[n][[All,2]]],{n,2,nn}];
%t q/.Table[Union[q][[i]]->i,{i,Length[Union[q]]}]
%o (PARI) a(n) = if (ispower(n,,&r), x = r, x = n); sum(k=2, x, ispower(k)==0); \\ _Michel Marcus_, Jul 19 2017
%Y Cf. A007916, A052409, A052410, A278028, A288636.
%K nonn
%O 2,2
%A _Gus Wiseman_, Jun 22 2017
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