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Numbers whose prime factors are 5 and 7.
14

%I #31 Dec 22 2020 03:49:08

%S 35,175,245,875,1225,1715,4375,6125,8575,12005,21875,30625,42875,

%T 60025,84035,109375,153125,214375,300125,420175,546875,588245,765625,

%U 1071875,1500625,2100875,2734375,2941225,3828125,4117715,5359375,7503125

%N Numbers whose prime factors are 5 and 7.

%C Numbers k such that phi(k)/k == 24/35. - _Artur Jasinski_, Nov 09 2008

%C Subsequence of A143202. - _Reinhard Zumkeller_, Sep 13 2011

%H Reinhard Zumkeller, <a href="/A033851/b033851.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 35*A003595(n). - _Artur Jasinski_, Nov 09 2008

%F A143201(a(n)) = 3. - _Reinhard Zumkeller_, Sep 13 2011

%F Sum_{n>=1} 1/a(n) = 1/24. - _Amiram Eldar_, Dec 22 2020

%t a = {}; Do[If[EulerPhi[x]/x == 24/35, AppendTo[a, x]], {x, 1, 10000}]; a (* _Artur Jasinski_, Nov 09 2008 *)

%t Take[With[{nn=10},Sort[Flatten[Table[5^i 7^j,{i,nn},{j,nn}]]]],40] (* _Harvey P. Dale_, Feb 09 2013 *)

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a033851 n = a033851_list !! (n-1)

%o a033851_list = f (singleton (5*7)) where

%o f s = m : f (insert (5*m) $ insert (7*m) s') where

%o (m,s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Sep 13 2011

%Y Cf. A003595, A147571-A147575, A147576-A147580. [_Artur Jasinski_, Nov 09 2008]

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

%Y Subsequence of A256617.

%K nonn

%O 1,1

%A _Jeff Burch_

%E Offset fixed by _Reinhard Zumkeller_, Sep 13 2011