OFFSET
1,2
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Henry Bottomley, Some Smarandache-type multiplicative sequences.
Eric Weisstein's World of Mathematics, Cubefree Part.
Eric Weisstein's World of Mathematics, Dirichlet Generating Function.
FORMULA
Multiplicative with p^e -> p^(e mod 3), p prime. - Reinhard Zumkeller, Nov 22 2009
Dirichlet g.f.: zeta(3s)*zeta(s-1)/zeta(3s-3). - R. J. Mathar, Feb 11 2011
a(n) = n/A008834(n). - R. J. Mathar, Dec 08 2015
Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / (1890*Zeta(3)). - Vaclav Kotesovec, Feb 08 2019
MAPLE
MATHEMATICA
cf[n_]:=Module[{tr=Transpose[FactorInteger[n]], ex, cb}, ex= tr[[2]]- Mod[ tr[[2]], 3]; cb=Times@@(First[#]^Last[#]&/@Transpose[{tr[[1]], ex}]); n/cb]; Array[cf, 75] (* Harvey P. Dale, Jun 03 2012 *)
f[p_, e_] := p^Mod[e, 3]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *)
PROG
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
def A050985(n):
return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(n).items()])
# Chai Wah Wu, Feb 04 2015
(PARI) a(n) = my(f=factor(n)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Eric W. Weisstein, Dec 11 1999
STATUS
approved