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

1,8

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Henry Bottomley, Some Smarandache-type multiplicative sequences.

Formula

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

Mathematica

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

Prog

(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
(Scheme)
(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

Crossrefs

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.

Sequence in context: A191358 A204133 A342017 * A073753 A290602 A255404

Adjacent sequences: A062375 A062376 A062377 * A062379 A062380 A062381

Keyword

nonn,mult

Author

Henry Bottomley, Jun 18 2001

Status

approved