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A052410 Write n = m^k with m, k integers, k >= 1, then a(n) = smallest possible choice for m. 15
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

CROSSREFS

Cf. A052409, A175781.

a(A001597(k))=A025478(k).

Cf. A027748, A124010.

Cf. A072775.

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

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Last modified March 26 20:49 EDT 2017. Contains 284137 sequences.