A175781 a(n) = n^(1/k) with the smallest k>1 such that n is a k-th power, taking k=1 if no such k>1 exists.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 4, 17, 18, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 8, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset: 1

Author

Vincenzo Librandi, Sep 03 2010

Keywords

• nonn

Examples

			a(32) = 2 since the least k, in this case 5, yields 32^(1/5) = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A052410.

Programs

Maple

f:= proc(n) local F,m;
     F:= ifactors(n)[2];
     m:= igcd(op(map(t->t[2],F)));
     if m = 1 then n
     else m:= min(numtheory:-factorset(m)); mul(t[1]^(t[2]/m),t=F)
     fi
end proc:
map(f, [$1..100]); # Robert Israel, Jan 10 2018

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; f[n_] := If[ perfectPowerQ@ n, k = 2; While[ !IntegerQ[n^(1/k)], k++]; n^(1/k), n]; Array[f, 75] (* Robert G. Wilson v, Jan 09 2018 *)

PARI

a(n) = my(p = ispower(n)); if (!p, n, sqrtnint(n, divisors(p)[2])); \\ Michel Marcus, Jan 02 2018

Extensions

Edited by the Associate Editors of the OEIS, Sep 03 2010

a(32) corrected by Gionata Neri, Jan 02 2018