OFFSET
1,2
COMMENTS
Value of m in m^p = n, where p is the largest possible power (see A052409).
For n > 1, n is a perfect power iff a(n) <> n. - Reinhard Zumkeller, Oct 13 2002
a(n)^A052409(n) = n. - Reinhard Zumkeller, Apr 06 2014
Every integer root of n is a power of a(n). All entries (except 1) belong to A007916. - Gus Wiseman, Sep 11 2017
LINKS
Daniel Forgues, Table of n, a(n) for n=1..100000
Eric Weisstein's World of Mathematics, Power
Eric Weisstein's World of Mathematics, Perfect Power
FORMULA
MAPLE
a:= n-> (l-> (t-> mul(i[1]^(i[2]/t), i=l))(
igcd(seq(i[2], i=l))))(ifactors(n)[2]):
seq(a(n), n=1..74); # Alois P. Heinz, Jul 22 2024
MATHEMATICA
Table[If[n==1, 1, n^(1/(GCD@@(Last/@FactorInteger[n])))], {n, 100}]
PROG
(Haskell)
a052410 n = product $ zipWith (^)
(a027748_row n) (map (`div` (foldl1 gcd es)) es)
where es = a124010_row n
-- Reinhard Zumkeller, Jul 15 2012
(PARI) a(n) = if (ispower(n, , &r), r, n); \\ Michel Marcus, Jul 19 2017
(Python)
def upto(n):
list = [1] + [0] * (n - 1)
for i in range(2, n + 1):
if not list[i - 1]:
j = i
while j <= n:
list[j - 1] = i
j *= i
return list
# M. Eren Kesim, Jun 03 2021
(Python)
from math import gcd
from sympy import integer_nthroot, factorint
def A052410(n): return integer_nthroot(n, gcd(*factorint(n).values()))[0] if n>1 else 1 # Chai Wah Wu, Mar 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition edited (in a complementary form to A052409) by Daniel Forgues, Mar 14 2009
Corrected by Charles R Greathouse IV, Sep 02 2009
Definition edited by N. J. A. Sloane, Sep 03 2010
STATUS
approved