cp's OEIS Frontend

A289023 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).

%I A289023 #18 May 04 2018 22:42:51
%S A289023 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 A289023 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 A289023 44,45,46,47,48,49,50,51,52,53,1,54,55,56,57,58,59,60
%N A289023 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 A289023 Every pair p of positive integers is of the form p = (a(n), A052409(n)) for exactly one n.
%F A289023 For n>1 we have a(n) = A278028(n,1).
%e A289023 a(27)=2 because the smallest root of 27 is 3, and 3 is the 2nd entry of A007916.
%e A289023 a(25)=3 because the smallest root of 25 is 5, and 5 is the 3rd entry of A007916.
%t A289023 nn=100;
%t A289023 q=Table[Power[n,1/GCD@@FactorInteger[n][[All,2]]],{n,2,nn}];
%t A289023 q/.Table[Union[q][[i]]->i,{i,Length[Union[q]]}]
%o A289023 (PARI) a(n) = if (ispower(n,,&r), x = r, x = n); sum(k=2, x, ispower(k)==0); \\ _Michel Marcus_, Jul 19 2017
%Y A289023 Cf. A007916, A052409, A052410, A278028, A288636.
%K A289023 nonn
%O A289023 2,2
%A A289023 _Gus Wiseman_, Jun 22 2017