A073753 -id:A073753 - cp's OEIS frontend

A062378 n divided by largest cubefree factor of n.

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, 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, 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

Offset: 1

Henry Bottomley, Jun 18 2001

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

Antti Karttunen, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.

Cf. A000189, A000578, A007948, A008834, A019555, A048798, A050985, A053149, A053150, A056551, A056552. See A003557 for squares and A062379 for 4th powers.
Differs from A073753 for the first time at n=90, where a(90) = 1, while A073753(90) = 3.
Cf. A007947, A055231.

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

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

(define (A062378 n) (/ n (A007948 n)))
(definec (A007948 n) (if (= 1 n) n (* (expt (A020639 n) (min 2 (A067029 n))) (A007948 (A028234 n)))))
;; Antti Karttunen, Nov 28 2017

a(n) = n / A007948(n).
a(n) = A003557(A003557(n)). - Antti Karttunen, Nov 28 2017
Multiplicative with a(p^e) = p^max(e-2, 0). - Amiram Eldar, Sep 07 2020
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

A073752 Greatest common divisor of n/spf(n) and n/gpf(n) where spf(n) is the smallest and gpf(n) is the greatest prime factor of n (see A020639, A006530).

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 3, 1, 16, 1, 1, 1, 6, 1, 1, 1, 4, 1, 3, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 6, 1, 1, 3, 32, 1, 3, 1, 2, 1, 5, 1, 12, 1, 1, 5, 2, 1, 3, 1, 8, 27, 1, 1, 6, 1, 1, 1, 4, 1, 9, 1, 2, 1, 1, 1, 16, 1, 7, 3, 10, 1

Offset: 1

Reinhard Zumkeller, Aug 07 2002

nonn

a(n) = if n=p^k (p prime, k>0) then p^(k-1) else n/(spf(n)*gpf(n)).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000961, A066048.

A073753(n) = a(a(n)).

gc[n_]:=Module[{fi=Transpose[FactorInteger[n]][[1]]},GCD[n/First[fi], n/Last[ fi]]]; Array[gc,110] (* Harvey P. Dale, Jun 17 2012 *)

a(n) = GCD(A032742(n), A052126(n)).

cp's OEIS Frontend

A062378 n divided by largest cubefree factor of n.

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