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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-Fran├žois 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.)