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 A052410 Write n = m^k with m, k integers, k >= 1, then a(n) is the smallest possible choice for m. 88
 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 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(A001597(k)) = A025478(k). 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 (Python) def upto(n):     list =  +  * (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 CROSSREFS Cf. A001597, A025478, A007916, A027748, A052409, A072775, A124010, A175781, A278028, A288636, A289023. Sequence in context: A019555 A243074 A304776 * A327501 A175781 A072775 Adjacent sequences:  A052407 A052408 A052409 * A052411 A052412 A052413 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

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Last modified May 22 19:45 EDT 2022. Contains 353957 sequences. (Running on oeis4.)