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A117992 Number of distinct rational numbers less than 1 that can be written as fractions of the first n composite numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
a(n) = (A117991(n) - 1)/2.
LINKS
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
Sequence in context: A056533 A329110 A114186 * A015614 A138203 A225523
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 08 2006
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)