A117992 - OEIS

%I #14 Mar 10 2019 08:51:23

%S 0,1,3,5,9,11,17,20,26,29,33,38,50,54,65,80,89,98,102,113,123,144,158,

%T 166,190,203,215,222,236,247,277,287,314,328,346,364,375,400,417,438,

%U 478,487,529,548,573,604,617,641,667,683,698,749,769,796,836,851,873

%N Number of distinct rational numbers less than 1 that can be written as fractions of the first n composite numbers.

%C a(n) = (A117991(n) - 1)/2.

%H Robert Israel, <a href="/A117992/b117992.txt">Table of n, a(n) for n = 1..6000</a>

%e n=4, the first 4 composite numbers are 4,6, 8 and 9:

%e a(3)=#{4/6,4/8,4/9,6/8,6/9,8/9}=#{4/9,1/2,2/3,3/4,8/9}=5.

%p N:= 1000: # to use composites up to N

%p comps:= remove(isprime, [$4..100]):

%p nc:= nops(comps):

%p S:= {}: A[1]:= 0:

%p for n from 2 to nc do

%p S:= S union {seq(comps[j]/comps[n],j=1..n-1)};

%p   A[n]:= nops(S);

%p od:

%p seq(A[i],i=1..nc); # _Robert Israel_, Jan 30 2018

%t M = 100; (* to use composites up to M *)

%t comps = Select[Range[4, M], CompositeQ];

%t nc = Length[comps]; S = {}; A[1] = 0;

%t For[n = 2, n <= nc, n++, S = S ~Union~ Table[comps[[j]]/comps[[n]], {j, 1, n - 1}]; A[n] = Length[S]];

%t Array[A, nc] (* _Jean-François Alcover_, Mar 10 2019, after _Robert Israel_ *)

%Y Cf. A015614, A117991.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Apr 08 2006