A033850 Numbers whose prime factors are 3 and 7.

21, 63, 147, 189, 441, 567, 1029, 1323, 1701, 3087, 3969, 5103, 7203, 9261, 11907, 15309, 21609, 27783, 35721, 45927, 50421, 64827, 83349, 107163, 137781, 151263, 194481, 250047, 321489, 352947, 413343, 453789, 583443, 750141, 964467

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

Numbers k such that phi(k)/k = 4/7, where phi is the Euler totient function A000010. - Lekraj Beedassy, Jul 18 2008

Subsequence of A143203. - Reinhard Zumkeller, Sep 13 2011

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 189, p. 57, Ellipses, Paris 2008.

Links

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

Crossrefs

Cf. A000010, A033845, A033846, A033847, A033848, A033849, A033851, A143203.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a033850 n = a033850_list !! (n-1)
a033850_list = f (singleton (3*7)) where
   f s = m : f (insert (3*m) $ insert (7*m) s') where
     (m,s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011

Mathematica

Select[Range[10^6],Union[FactorInteger[#][[;;,1]]]=={3,7}&] (* Harvey P. Dale, Mar 01 2023 *)

Formula

A143201(a(n)) = 5. - Reinhard Zumkeller, Sep 13 2011

Sum_{n>=1} 1/a(n) = 1/12. - Amiram Eldar, Dec 22 2020

Extensions

Offset fixed by Reinhard Zumkeller, Sep 13 2011