A117992 Number of distinct rational numbers less than 1 that can be written as fractions of the first n composite numbers.

0, 1, 3, 5, 9, 11, 17, 20, 26, 29, 33, 38, 50, 54, 65, 80, 89, 98, 102, 113, 123, 144, 158, 166, 190, 203, 215, 222, 236, 247, 277, 287, 314, 328, 346, 364, 375, 400, 417, 438, 478, 487, 529, 548, 573, 604, 617, 641, 667, 683, 698, 749, 769, 796, 836, 851, 873

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2006

Keywords

• nonn

Comments

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..6000

Crossrefs

Cf. A015614, A117991.

Programs

Maple

N:= 1000: # to use composites up to N
comps:= remove(isprime, [$4..100]):
nc:= nops(comps):
S:= {}: A[1]:= 0:
for n from 2 to nc do
S:= S union {seq(comps[j]/comps[n],j=1..n-1)};
  A[n]:= nops(S);
od:
seq(A[i],i=1..nc); # Robert Israel, Jan 30 2018

Mathematica

M = 100; (* to use composites up to M *)
comps = Select[Range[4, M], CompositeQ];
nc = Length[comps]; S = {}; A[1] = 0;
For[n = 2, n <= nc, n++, S = S ~Union~ Table[comps[[j]]/comps[[n]], {j, 1, n - 1}]; A[n] = Length[S]];
Array[A, nc] (* Jean-François Alcover, Mar 10 2019, after Robert Israel *)