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A056552 Powerfree kernel of cubefree part of n. 7
1, 2, 3, 2, 5, 6, 7, 1, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 3, 5, 26, 1, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 5, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 2, 55, 7, 57, 58, 59, 30, 61, 62, 21, 1, 65, 66, 67, 34, 69, 70, 71, 3, 73, 74, 15, 38, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n=Product[Pj^Ej] then a(n)=Product[Pj^Fj], where Fj=0 if Ej is 0 or a multiple of 3 and Fj=1 otherwise.

Multiplicative with a(p^e) = p^(if 3|e, then 0, else 1). - Mitch Harris, Apr 19 2005

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

H. Bottomley, Some Smarandache-type multiplicative sequences

FORMULA

a(n) = A007947(A050985(n)) = A019555(A050985(n)) = n/(A053150(n)*A000189(n)) = A019555(n)/A053150(n) = A056551(n)^(1/3).

EXAMPLE

a(32)=2 because cubefree part of 32 is 4 and powerfree kernel of 4 is 2.

MATHEMATICA

f[p_, e_] :=  p^If[Divisible[e, 3], 0, 1]; a[n_] := Times @@ (f @@@ FactorInteger[ n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

PROG

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, if (frac(f[k, 2]/3), f[k, 2] = 1, f[k, 2] = 0)); factorback(f); \\ Michel Marcus, Feb 28 2019

CROSSREFS

Cf. A000189, A000578, A007947, A008834, A019555, A048798, A050985, A053149, A053150, A056551.

Sequence in context: A088861 A088631 A086184 * A049273 A053590 A208644

Adjacent sequences:  A056549 A056550 A056551 * A056553 A056554 A056555

KEYWORD

nonn,mult

AUTHOR

Henry Bottomley, Jun 25 2000

STATUS

approved

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