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 A055229 Greatest common divisor of largest square dividing n and squarefree part of n. 34
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 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, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Record values occur at cubes of squarefree numbers: a(A062838(n))=A005117(n) and a(m) < A005117(n) for m < A062838(n). -  Reinhard Zumkeller, Apr 09 2010 A220218(a(n)) = 1; A060476(a(n)) > 1 for n > 1. - Reinhard Zumkeller, Nov 30 2015 LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = gcd[A008833(n), A007913(n)] Multiplicative with a(p^e)=1 for even e, a(p)=1, a(p^e)=p for odd e>1. - Vladeta Jovovic, Apr 30 2002 a(n) = core(n)*rad(n/core(n))/rad(n), where core = A007913 and rad = A007947. - Conjecture by Velin Yanev, proof by David J. Seal, Sep 19 2017 MATHEMATICA a[n_] := With[{sf = Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[n])}, GCD[sf, n/sf]]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Feb 05 2014 *) PROG (PARI) a(n)=my(c=core(n)); gcd(c, n/c) \\ Charles R Greathouse IV, Nov 20 2012 (Haskell) a055229 n = product \$ zipWith (^) ps (map (flip mod 2) es) where    (ps, es) = unzip \$               filter ((> 1) . snd) \$ zip (a027748_row n) (a124010_row n) -- Reinhard Zumkeller, Oct 27 2015 CROSSREFS Cf. A008833, A007913, A000188. Cf. A027748, A124010, A060476, A220218. Sequence in context: A307427 A318672 A325989 * A270419 A275216 A062379 Adjacent sequences:  A055226 A055227 A055228 * A055230 A055231 A055232 KEYWORD nice,nonn,mult AUTHOR Labos Elemer, Jun 21 2000 STATUS approved

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Last modified September 23 16:17 EDT 2020. Contains 337314 sequences. (Running on oeis4.)