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A033849
Numbers whose prime factors are 3 and 5.
27
15, 45, 75, 135, 225, 375, 405, 675, 1125, 1215, 1875, 2025, 3375, 3645, 5625, 6075, 9375, 10125, 10935, 16875, 18225, 28125, 30375, 32805, 46875, 50625, 54675, 84375, 91125, 98415, 140625, 151875, 164025, 234375, 253125, 273375, 295245
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
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