OFFSET
1,1
COMMENTS
Numbers k such that phi(k) = (8/15)*k. - Benoit Cloitre, Apr 19 2002
Subsequence of A143202. - Reinhard Zumkeller, Sep 13 2011
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
From Reinhard Zumkeller, Sep 13 2011: (Start)
A143201(a(n)) = 3.
a(n) = 15*A003593(n). (End)
Sum_{n>=1} 1/a(n) = 1/8. - Amiram Eldar, Dec 22 2020
MATHEMATICA
Sort[Flatten[Table[Table[3^j*5^k, {j, 1, 10}], {k, 1, 10}]]] (* Geoffrey Critzer, Dec 07 2014 *)
Select[Range[300000], FactorInteger[#][[All, 1]]=={3, 5}&] (* Harvey P. Dale, Oct 19 2022 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a033849 n = a033849_list !! (n-1)
a033849_list = f (singleton (3*5)) where
f s = m : f (insert (3*m) $ insert (5*m) s') where
(m, s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011
(Python)
from sympy import integer_log
def A033849(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum(integer_log(x//5**i, 3)[0]+1 for i in range(integer_log(x, 5)[0]+1))
return 15*bisection(f, n, n) # Chai Wah Wu, Oct 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset and typo in data fixed by Reinhard Zumkeller, Sep 13 2011
STATUS
approved