

A052410


Write n = m^k with m, k integers, k >= 1, then a(n) = smallest possible choice for m.


19



1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 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, 2, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
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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

a(n) = A007916(A278028(n,1)).  Gus Wiseman, Sep 11 2017


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


CROSSREFS

Cf. a(A001597(k)) = A025478(k), A007916, A027748, A052409, A072775, A124010, A175781, A278028, A288636, A289023.
Sequence in context: A166140 A019555 A243074 * A175781 A072775 A243057
Adjacent sequences: A052407 A052408 A052409 * A052411 A052412 A052413


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


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



