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

1,3

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A015614, A117991.

Sequence in context: A056533 A329110 A114186 * A015614 A138203 A225523

Adjacent sequences: A117989 A117990 A117991 * A117993 A117994 A117995

Keyword

nonn

Author

Reinhard Zumkeller, Apr 08 2006

Status

approved