A033846 Numbers whose prime factors are 2 and 5.

10, 20, 40, 50, 80, 100, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1250, 1280, 1600, 2000, 2500, 2560, 3200, 4000, 5000, 5120, 6250, 6400, 8000, 10000, 10240, 12500, 12800, 16000, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• easy

Comments

Numbers k such that Sum_{d prime divisor of k} 1/d = 7/10. - Benoit Cloitre, Apr 13 2002

Numbers k such that phi(k) = (2/5)*k. - Benoit Cloitre, Apr 19 2002

Numbers k such that Sum_{d|k} A008683(d)*A000700(d) = 7. - Carl Najafi, Oct 20 2011

Links

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

Crossrefs

Cf. A033845, A033847, A033848, A033849, A033850, A033851, A003592.

Cf. A086780, A143201.

Cf. A000700, A008683.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a033846 n = a033846_list !! (n-1)
a033846_list = f (singleton (2*5)) where
   f s = m : f (insert (2*m) $ insert (5*m) s') where
     (m,s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011

Magma

[n:n in [1..100000]| Set(PrimeDivisors(n)) eq {2,5}]; // Marius A. Burtea, May 10 2019

Maple

A033846 := proc(n)
if (numtheory[factorset](n) = {2,5}) then
   RETURN(n)
fi: end:  seq(A033846(n),n=1..50000); # Jani Melik, Feb 24 2011

Mathematica

Take[Union[Times@@@Select[Flatten[Table[Tuples[{2,5},n],{n,2,15}],1], Length[Union[#]]>1&]],45] (* Harvey P. Dale, Dec 15 2011 *)

PARI

isA033846(n)=factor(n)[,1]==[2,5]~ \\ Charles R Greathouse IV, Feb 24 2011

Formula

a(n) = 10*A003592(n).

A143201(a(n)) = 4. - Reinhard Zumkeller, Sep 13 2011

Sum_{n>=1} 1/a(n) = 1/4. - Amiram Eldar, Dec 22 2020

Extensions

Offset fixed by Reinhard Zumkeller, Sep 13 2011