A008834 Largest cube dividing n.

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

Offset

1,8

Links

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

Henry 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]). - Mitch Harris, Apr 19 2005

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

a(n) = n/A050985(n). - Amiram Eldar, Aug 15 2023

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-François 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

Cf. A000203, A050985, A053150.

Sequence in context: A368540 A103760 A268355 * A368170 A366906 A056201

Adjacent sequences: A008831 A008832 A008833 * A008835 A008836 A008837

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved