A036311 - OEIS

%I #28 May 18 2022 07:56:48

%S 4,8,10,16,20,25,32,40,50,64,80,100,125,128,160,200,250,256,320,400,

%T 500,512,625,640,800,1000,1024,1250,1280,1600,2000,2048,2500,2560,

%U 3125,3200,4000,4096,5000,5120,6250,6400,8000,8192,10000,10240,12500,12800

%N Composite numbers whose prime factors contain no digits other than 2 and 5.

%C A003592 with 1, 2 and 5 removed. - _Robert Israel_, Apr 29 2018

%H Robert Israel, <a href="/A036311/b036311.txt">Table of n, a(n) for n = 1..10000</a> (first 131 terms from Vincenzo Librandi)

%H <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.

%F Sum_{n>=1} 1/a(n) = 4/5. - _Amiram Eldar_, May 18 2022~

%p N:= 20000: # to get all terms <= N

%p S:= {seq(seq(2^i*5^j,i=0..ilog2(N/5^j)),j=0..floor(log[5](N)))} minus {1,2,5}:

%p sort(convert(S,list)); # _Robert Israel_, Apr 29 2018

%t dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {2}||d == {5}||d == {2, 5})]; Select[Range[15000], dpfQ] (* _Vincenzo Librandi_, Aug 25 2013 *)

%o (Magma) [n: n in [4..13000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [2,5]}]; // _Bruno Berselli_, Aug 26 2013

%Y Cf. A003592, A036302-A036325, A025612.

%K nonn,easy,base

%O 1,1

%A _Patrick De Geest_, Dec 15 1998