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
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
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
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} ((p^3 + p^2 + p - 1)/(p^2 * (p + 1))) = 1.2249749939341923764... . - Amiram Eldar, Oct 08 2022
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
KEYWORD
nice,nonn,mult
AUTHOR
Labos Elemer, Jun 21 2000
STATUS
approved