|
|
A065330
|
|
a(n) = max { k | gcd(n, k) = k and gcd(k, 6) = 1 }.
|
|
25
|
|
|
1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 1, 25, 13, 1, 7, 29, 5, 31, 1, 11, 17, 35, 1, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 1, 49, 25, 17, 13, 53, 1, 55, 7, 19, 29, 59, 5, 61, 31, 7, 1, 65, 11, 67, 17, 23, 35, 71, 1, 73, 37, 25, 19, 77, 13, 79, 5, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(2^e)=1, a(3^e)=1, a(p^e)=p^e, p>3. - Vladeta Jovovic, Nov 02 2001
a(1)=1; then a(2n)=a(n), a(2n+1)=a((2n+1)/3) if 2n+1 is divisible by 3, a(2n+1)=2n+1 otherwise. - Benoit Cloitre, Jun 04 2007
Dirichlet g.f. zeta(s-1)*(1-2^(1-s))*(1-3^(1-s))/ ( (1-2^(-s))*(1-3^(-s)) ). - R. J. Mathar, Jul 04 2011
Sum_{k=1..n} a(k) ~ (1/4) * n^2. - Amiram Eldar, Oct 22 2022
|
|
EXAMPLE
|
a(30) = 5.
|
|
MAPLE
|
local a, f, p, e ;
a := 1 ;
for f in ifactors(n)[2] do
p := op(1, f) ;
e := op(2, f) ;
if p > 3 then
a := a*p^e ;
end if;
end do:
a ;
with(padic): a := n -> n/(2^ordp(n, 2)*3^ordp(n, 3));
|
|
MATHEMATICA
|
f[n_] := Times @@ (First@#^Last@# & /@ Select[FactorInteger@n, First@# != 2 && First@# != 3 &]); Array[f, 81] (* Robert G. Wilson v, Aug 18 2006 *)
|
|
PROG
|
(PARI) a(n)=if(n<2, 1, if(n%2, if(n%3, n, a(n/3)), a(n/2))) \\ Benoit Cloitre, Jun 04 2007
(PARI) a(n)=n\gcd(n, 6^n) \\ Not very efficient, but simple. Stanislav Sykora, Feb 08 2016
(Haskell)
|
|
CROSSREFS
|
|
|
KEYWORD
|
mult,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|