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A033846 Numbers whose prime factors are 2 and 5.

%I A033846 #58 Feb 13 2024 06:56:01
%S A033846 10,20,40,50,80,100,160,200,250,320,400,500,640,800,1000,1250,1280,
%T A033846 1600,2000,2500,2560,3200,4000,5000,5120,6250,6400,8000,10000,10240,
%U A033846 12500,12800,16000,20000,20480,25000,25600,31250,32000,40000,40960
%N A033846 Numbers whose prime factors are 2 and 5.
%C A033846 Numbers k such that Sum_{d prime divisor of k} 1/d = 7/10. - _Benoit Cloitre_, Apr 13 2002
%C A033846 Numbers k such that phi(k) = (2/5)*k. - _Benoit Cloitre_, Apr 19 2002
%C A033846 Numbers k such that Sum_{d|k} A008683(d)*A000700(d) = 7. - _Carl Najafi_, Oct 20 2011
%H A033846 Reinhard Zumkeller, <a href="/A033846/b033846.txt">Table of n, a(n) for n = 1..10000</a>
%F A033846 a(n) = 10*A003592(n).
%F A033846 A143201(a(n)) = 4. - _Reinhard Zumkeller_, Sep 13 2011
%F A033846 Sum_{n>=1} 1/a(n) = 1/4. - _Amiram Eldar_, Dec 22 2020
%p A033846 A033846 := proc(n)
%p A033846 if (numtheory[factorset](n) = {2,5}) then
%p A033846    RETURN(n)
%p A033846 fi: end:  seq(A033846(n),n=1..50000); # _Jani Melik_, Feb 24 2011
%t A033846 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 A033846 (PARI) isA033846(n)=factor(n)[,1]==[2,5]~ \\ _Charles R Greathouse IV_, Feb 24 2011
%o A033846 (Haskell)
%o A033846 import Data.Set (singleton, deleteFindMin, insert)
%o A033846 a033846 n = a033846_list !! (n-1)
%o A033846 a033846_list = f (singleton (2*5)) where
%o A033846    f s = m : f (insert (2*m) $ insert (5*m) s') where
%o A033846      (m,s') = deleteFindMin s
%o A033846 -- _Reinhard Zumkeller_, Sep 13 2011
%o A033846 (Magma) [n:n in [1..100000]| Set(PrimeDivisors(n)) eq {2,5}]; // _Marius A. Burtea_, May 10 2019
%Y A033846 Cf. A033845, A033847, A033848, A033849, A033850, A033851, A003592.
%Y A033846 Cf. A086780, A143201.
%Y A033846 Cf. A000700, A008683.
%K A033846 nonn,easy
%O A033846 1,1
%A A033846 _Jeff Burch_
%E A033846 Offset fixed by _Reinhard Zumkeller_, Sep 13 2011