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 A062378 n divided by largest cubefree factor of n. 10

%I

%S 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,2,1,1,3,1,1,1,1,8,1,1,

%T 1,1,1,1,1,2,1,1,1,1,1,1,1,4,1,1,1,1,1,3,1,2,1,1,1,1,1,1,1,16,1,1,1,1,

%U 1,1,1,2,1,1,1,1,1,1,1,4,9,1,1,1,1,1,1,2,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,2

%N n divided by largest cubefree factor of n.

%C Numerator of n/rad(n)^2, where rad is the squarefree kernel of n (A007947), denominator: A055231. - _Reinhard Zumkeller_, Dec 10 2002

%H Antti Karttunen, <a href="/A062378/b062378.txt">Table of n, a(n) for n = 1..10000</a>

%H Henry Bottomley, <a href="http://fs.gallup.unm.edu/Bottomley-Sm-Mult-Functions.htm">Some Smarandache-type multiplicative sequences</a>.

%F a(n) = n / A007948(n).

%F a(n) = A003557(A003557(n)). - _Antti Karttunen_, Nov 28 2017

%F Multiplicative with a(p^e) = p^max(e-2, 0). - _Amiram Eldar_, Sep 07 2020

%t f[p_, e_] := p^Max[e-2, 0]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Sep 07 2020 *)

%o (PARI) a(n)=my(f=factor(n));prod(i=1,#f~,f[i,1]^max(f[i,2]-2,0)) \\ _Charles R Greathouse IV_, Aug 08 2013

%o (Scheme)

%o (define (A062378 n) (/ n (A007948 n)))

%o (definec (A007948 n) (if (= 1 n) n (* (expt (A020639 n) (min 2 (A067029 n))) (A007948 (A028234 n)))))

%o ;; _Antti Karttunen_, Nov 28 2017

%Y Cf. A000189, A000578, A007948, A008834, A019555, A048798, A050985, A053149, A053150, A056551, A056552. See A003557 for squares and A062379 for 4th powers.

%Y Differs from A073753 for the first time at n=90, where a(90) = 1, while A073753(90) = 3.

%Y Cf. A007947, A055231.

%K nonn,mult

%O 1,8

%A _Henry Bottomley_, Jun 18 2001

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)