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
(Python)
from math import prod
from sympy import factorint
def A008834(n): return prod(p**(e-e%3) for p, e in factorint(n).items()) # Chai Wah Wu, Aug 08 2024
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved