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 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-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 Sequence in context: A056191 A103760 A268355 * A056201 A088842 A284098 Adjacent sequences:  A008831 A008832 A008833 * A008835 A008836 A008837 KEYWORD nonn,easy,mult AUTHOR STATUS approved

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