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 A052409 a(n) = largest integer power m for which a representation of the form n = k^m exists (for some k). 105
 0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Greatest common divisor of all prime-exponents in canonical factorization of n for n>1: a(n)>1 iff n is a perfect power; a(A001597(k))=A025479(k). - Reinhard Zumkeller, Oct 13 2002 a(1) set to 0 since there is no largest finite integer power m for which a representation of the form 1 = 1^m exists (infinite largest m). - Daniel Forgues, Mar 06 2009 A052410(n)^a(n) = n. - Reinhard Zumkeller, Apr 06 2014 Positions of 1's are A007916. Smallest base is given by A052410. - Gus Wiseman, Jun 09 2020 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(1) = 0; for n > 1, a(n) = gcd(A067029(n), a(A028234(n))). - Antti Karttunen, Aug 07 2017 EXAMPLE n = 72 = 2*2*2*3*3: GCD[exponents] = GCD[3,2] = 1. This is the least n for which a(n) <> A051904(n), the minimum of exponents. For n = 10800 = 2^4 * 3^3 * 5^2, GCD[4,3,2] = 1, thus a(10800) = 1. MAPLE # See link. # a:= n-> igcd(map(i-> i[2], ifactors(n)[2])[]): seq(a(n), n=1..120);  # Alois P. Heinz, Oct 20 2019 MATHEMATICA Table[GCD @@ Last /@ FactorInteger[n], {n, 100}] (* Ray Chandler, Jan 24 2006 *) PROG (Haskell) a052409 1 = 0 a052409 n = foldr1 gcd \$ a124010_row n -- Reinhard Zumkeller, May 26 2012 (PARI) a(n)=my(k=ispower(n)); if(k, k, n>1) \\ Charles R Greathouse IV, Oct 30 2012 (Scheme) (define (A052409 n) (if (= 1 n) 0 (gcd (A067029 n) (A052409 (A028234 n))))) ;; Antti Karttunen, Aug 07 2017 CROSSREFS Cf. A052410, A005361, A051903, A072411-A072414, A124010, A075802, A072776, A270492. Apart from the initial term essentially the same as A253641. Differs from A051904 for the first time at n=72, where a(72) = 1, while A051904(72) = 2. Differs from A158378 for the first time at n=10800, where a(10800) = 1, while A158378(10800) = 2. Cf. A000005, A000961, A001597, A052410, A303386, A327501. Sequence in context: A158052 A253641 A158378 * A051904 A070012 A071178 Adjacent sequences:  A052406 A052407 A052408 * A052410 A052411 A052412 KEYWORD nonn AUTHOR EXTENSIONS More terms from Labos Elemer, Jun 17 2002 STATUS approved

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Last modified December 4 18:29 EST 2020. Contains 338936 sequences. (Running on oeis4.)