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 A055229 Greatest common divisor of largest square dividing n and squarefree part of n. 34

%I

%S 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,

%T 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,

%U 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

%N Greatest common divisor of largest square dividing n and squarefree part of n.

%C 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

%C A220218(a(n)) = 1; A060476(a(n)) > 1 for n > 1. - _Reinhard Zumkeller_, Nov 30 2015

%H R. Zumkeller, <a href="/A055229/b055229.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = gcd[A008833(n), A007913(n)]

%F 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

%F 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

%t 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 *)

%o (PARI) a(n)=my(c=core(n));gcd(c,n/c) \\ _Charles R Greathouse IV_, Nov 20 2012

%o a055229 n = product \$ zipWith (^) ps (map (flip mod 2) es) where

%o (ps, es) = unzip \$

%o filter ((> 1) . snd) \$ zip (a027748_row n) (a124010_row n)

%o -- _Reinhard Zumkeller_, Oct 27 2015

%Y Cf. A008833, A007913, A000188.

%Y Cf. A027748, A124010, A060476, A220218.

%K nice,nonn,mult

%O 1,8

%A _Labos Elemer_, Jun 21 2000

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)