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Numbers whose prime factors are 2 and 5.
23

%I #58 Feb 13 2024 06:56:01

%S 10,20,40,50,80,100,160,200,250,320,400,500,640,800,1000,1250,1280,

%T 1600,2000,2500,2560,3200,4000,5000,5120,6250,6400,8000,10000,10240,

%U 12500,12800,16000,20000,20480,25000,25600,31250,32000,40000,40960

%N Numbers whose prime factors are 2 and 5.

%C Numbers k such that Sum_{d prime divisor of k} 1/d = 7/10. - _Benoit Cloitre_, Apr 13 2002

%C Numbers k such that phi(k) = (2/5)*k. - _Benoit Cloitre_, Apr 19 2002

%C Numbers k such that Sum_{d|k} A008683(d)*A000700(d) = 7. - _Carl Najafi_, Oct 20 2011

%H Reinhard Zumkeller, <a href="/A033846/b033846.txt">Table of n, a(n) for n = 1..10000</a>

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

%F A143201(a(n)) = 4. - _Reinhard Zumkeller_, Sep 13 2011

%F Sum_{n>=1} 1/a(n) = 1/4. - _Amiram Eldar_, Dec 22 2020

%p A033846 := proc(n)

%p if (numtheory[factorset](n) = {2,5}) then

%p RETURN(n)

%p fi: end: seq(A033846(n),n=1..50000); # _Jani Melik_, Feb 24 2011

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

%o (PARI) isA033846(n)=factor(n)[,1]==[2,5]~ \\ _Charles R Greathouse IV_, Feb 24 2011

%o (Haskell)

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

%o a033846 n = a033846_list !! (n-1)

%o a033846_list = f (singleton (2*5)) where

%o f s = m : f (insert (2*m) $ insert (5*m) s') where

%o (m,s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Sep 13 2011

%o (Magma) [n:n in [1..100000]| Set(PrimeDivisors(n)) eq {2,5}]; // _Marius A. Burtea_, May 10 2019

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

%Y Cf. A086780, A143201.

%Y Cf. A000700, A008683.

%K nonn,easy

%O 1,1

%A _Jeff Burch_

%E Offset fixed by _Reinhard Zumkeller_, Sep 13 2011