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

Author

Jeff Burch

Keywords

• nonn

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

Crossrefs

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

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

Subsequence of A256617.

Programs

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

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 *)

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

Extensions

Offset fixed by Reinhard Zumkeller, Sep 13 2011