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%I #34 Dec 07 2023 01:44:16
%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
%F Dirichlet g.f.: zeta(s-1) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^s - 1/p^(2*s-1) + 1/p^(2*s)). - _Amiram Eldar_, Dec 07 2023
%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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