login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008834 Largest cube dividing n. 12
1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 27, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 27, 1, 8, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Multiplicative with a(p^e) = p^(3[e/3]). - Mitch Harris, Apr 19 2005

LINKS

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

H. Bottomley, Some Smarandache-type multiplicative sequences

Vaclav Kotesovec, Graph - the asymptotic ratio

Eric Weisstein's World of Mathematics, Cubic Part

FORMULA

Multiplicative with a(p^e) = p^(3[e/3]).

a(n) = A053150(n)^3. - R. J. Mathar, May 27 2011

Dirichlet g.f.: zeta(s)*zeta(3s-3)/zeta(3s). The Dirichlet convolution of this sequence with A050985 generates A000203. - R. J. Mathar, Apr 05 2011

Sum_{k=1..n} a(k) ~ 45 * Zeta(4/3) * n^(4/3) / (2*Pi^4). - Vaclav Kotesovec, Jan 31 2019

MAPLE

with(numtheory): [ seq( expand(nthpow(i, 3)), i=1..200) ];

# alternative:

A008834 := proc(n)

    local p;

    a := 1 ;

    for p in ifactors(n)[2] do

        e := floor(op(2, p)/3) ;

        a := a*op(1, p)^(3*e) ;

    end do:

    a ;

end proc:

seq(A008834(n), n=1..40) ; # R. J. Mathar, Dec 08 2015

MATHEMATICA

a[n_] := Times @@ (#[[1]]^(#[[2]] - Mod[#[[2]], 3]) & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 81}]

(* Jean-Fran├žois Alcover, Jul 31 2011, after PARI prog. *)

  upto=1000; Flatten[With[{c=Range[Floor[Surd[upto, 3]], 1, -1]^3}, Table[ Select[ c, Divisible[n, #]&, 1], {n, upto}]]](* Harvey P. Dale, Apr 07 2013 *)

PROG

(PARI) a(n)=n=factor(n); prod(i=1, #n[, 1]; n[i, 1]^(n[i, 2]\3*3)) \\ Charles R Greathouse IV, Jul 28 2011

CROSSREFS

Sequence in context: A056191 A103760 A268355 * A056201 A088842 A284098

Adjacent sequences:  A008831 A008832 A008833 * A008835 A008836 A008837

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)