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).

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, 23, 24, 1, 25, 26, 27, 4, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 5, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 1, 54, 55, 56, 57, 58, 59, 60

Offset: 2

Author

Gus Wiseman, Jun 22 2017

Keywords

• nonn

Comments

Every pair p of positive integers is of the form p = (a(n), A052409(n)) for exactly one n.

Examples

			a(27)=2 because the smallest root of 27 is 3, and 3 is the 2nd entry of A007916.
a(25)=3 because the smallest root of 25 is 5, and 5 is the 3rd entry of A007916.
		

Crossrefs

Cf. A007916, A052409, A052410, A278028, A288636.

Programs

Mathematica

nn=100;
q=Table[Power[n,1/GCD@@FactorInteger[n][[All,2]]],{n,2,nn}];
q/.Table[Union[q][[i]]->i,{i,Length[Union[q]]}]

PARI

a(n) = if (ispower(n,,&r), x = r, x = n); sum(k=2, x, ispower(k)==0); \\ Michel Marcus, Jul 19 2017

Formula

For n>1 we have a(n) = A278028(n,1).