A033851 Numbers whose prime factors are 5 and 7.

35, 175, 245, 875, 1225, 1715, 4375, 6125, 8575, 12005, 21875, 30625, 42875, 60025, 84035, 109375, 153125, 214375, 300125, 420175, 546875, 588245, 765625, 1071875, 1500625, 2100875, 2734375, 2941225, 3828125, 4117715, 5359375, 7503125

Offset

1,1

Comments

Numbers k such that phi(k)/k == 24/35. - Artur Jasinski, Nov 09 2008

Subsequence of A143202. - Reinhard Zumkeller, Sep 13 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = 35*A003595(n). - Artur Jasinski, Nov 09 2008

A143201(a(n)) = 3. - Reinhard Zumkeller, Sep 13 2011

Sum_{n>=1} 1/a(n) = 1/24. - Amiram Eldar, Dec 22 2020

Mathematica

a = {}; Do[If[EulerPhi[x]/x == 24/35, AppendTo[a, x]], {x, 1, 10000}]; a (* Artur Jasinski, Nov 09 2008 *)
Take[With[{nn=10}, Sort[Flatten[Table[5^i 7^j, {i, nn}, {j, nn}]]]], 40] (* Harvey P. Dale, Feb 09 2013 *)

Prog

(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a033851 n = a033851_list !! (n-1)
a033851_list = f (singleton (5*7)) where
   f s = m : f (insert (5*m) $ insert (7*m) s') where
     (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011

Crossrefs

Cf. A003595, A147571-A147575, A147576-A147580. [Artur Jasinski, Nov 09 2008]

Cf. A033845, A033846, A033847, A033848, A033849, A033850, A143201, A143202.

Subsequence of A256617.

Sequence in context: A228453 A327651 A319042 * A219825 A194716 A220047

Adjacent sequences: A033848 A033849 A033850 * A033852 A033853 A033854

Keyword

nonn

Author

Jeff Burch

Extensions

Offset fixed by Reinhard Zumkeller, Sep 13 2011

Status

approved