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A117992
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Number of distinct rational numbers less than 1 that can be written as fractions of the first n composite numbers.
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2
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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
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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