cp's OEIS Frontend

A033849 Numbers whose prime factors are 3 and 5.

%I A033849 #36 Oct 22 2024 15:16:39
%S A033849 15,45,75,135,225,375,405,675,1125,1215,1875,2025,3375,3645,5625,6075,
%T A033849 9375,10125,10935,16875,18225,28125,30375,32805,46875,50625,54675,
%U A033849 84375,91125,98415,140625,151875,164025,234375,253125,273375,295245
%N A033849 Numbers whose prime factors are 3 and 5.
%C A033849 Numbers k such that phi(k) = (8/15)*k. - _Benoit Cloitre_, Apr 19 2002
%C A033849 Subsequence of A143202. - _Reinhard Zumkeller_, Sep 13 2011
%H A033849 Reinhard Zumkeller, <a href="/A033849/b033849.txt">Table of n, a(n) for n = 1..10000</a>
%F A033849 From _Reinhard Zumkeller_, Sep 13 2011: (Start)
%F A033849 A143201(a(n)) = 3.
%F A033849 a(n) = 15*A003593(n). (End)
%F A033849 Sum_{n>=1} 1/a(n) = 1/8. - _Amiram Eldar_, Dec 22 2020
%t A033849 Sort[Flatten[Table[Table[3^j*5^k, {j, 1, 10}], {k, 1, 10}]]] (* _Geoffrey Critzer_, Dec 07 2014 *)
%t A033849 Select[Range[300000],FactorInteger[#][[All,1]]=={3,5}&] (* _Harvey P. Dale_, Oct 19 2022 *)
%o A033849 (Haskell)
%o A033849 import Data.Set (singleton, deleteFindMin, insert)
%o A033849 a033849 n = a033849_list !! (n-1)
%o A033849 a033849_list = f (singleton (3*5)) where
%o A033849    f s = m : f (insert (3*m) $ insert (5*m) s') where
%o A033849      (m,s') = deleteFindMin s
%o A033849 -- _Reinhard Zumkeller_, Sep 13 2011
%o A033849 (Python)
%o A033849 from sympy import integer_log
%o A033849 def A033849(n):
%o A033849     def bisection(f,kmin=0,kmax=1):
%o A033849         while f(kmax) > kmax: kmax <<= 1
%o A033849         while kmax-kmin > 1:
%o A033849             kmid = kmax+kmin>>1
%o A033849             if f(kmid) <= kmid:
%o A033849                 kmax = kmid
%o A033849             else:
%o A033849                 kmin = kmid
%o A033849         return kmax
%o A033849     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))
%o A033849     return 15*bisection(f,n,n) # _Chai Wah Wu_, Oct 22 2024
%Y A033849 Cf. A033845, A033846, A033847, A033848, A033850, A033851, A143201, A143202.
%Y A033849 Subsequence of A256617.
%K A033849 nonn
%O A033849 1,1
%A A033849 _Jeff Burch_
%E A033849 Offset and typo in data fixed by _Reinhard Zumkeller_, Sep 13 2011