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A218993
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Numerator of the least reduced fraction b/c > 1 using divisors b and c of n.
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4
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2, 3, 2, 5, 3, 7, 2, 3, 2, 11, 4, 13, 2, 5, 2, 17, 3, 19, 5, 7, 2, 23, 4, 5, 2, 3, 7, 29, 6, 31, 2, 3, 2, 7, 4, 37, 2, 3, 5, 41, 7, 43, 2, 5, 2, 47, 4, 7, 2, 3, 2, 53, 3, 11, 8, 3, 2, 59, 6, 61, 2, 9, 2, 13, 3, 67, 2, 3, 7, 71, 9, 73, 2, 5, 2, 11, 3, 79, 5, 3, 2
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OFFSET
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2,1
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COMMENTS
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The product b*c divides n. Does every positive integer except one occur infinitely many times?
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LINKS
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EXAMPLE
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For n = 2,...,12, the fractions are 2/1, 3/1, 2/1, 5/1, 3/2, 7/1, 2/1, 3/1, 2/1, 11/1, 4/3, so that
A218993 = (2, 3, 2, 5, 3, 7, 2, 3, 2, 11, 4, ... );
A219093 = (1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, ... );
A219094 = (1, 1, 2, 1, 1, 1, 4, 3, 5, 1, 1, ... );
A219095 = (6, 12, 15, 18, 20, 21, 24, 28, 30, 35, 36, ... ).
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MATHEMATICA
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f[n_] := Divisors[n];
t = Table[Min[Table[f[n][[i + 1]]/f[n][[i]], {i, 1, -1 + Length[f[n]]}]], {n, 2, 200}];
Table[n/(tn[[n - 1]]*td[[n - 1]]),
p[n_] := If[IntegerQ[t[[n]]], 0, 1]
u = Table[p[n], {n, 1, Length[t]}]; 1 + Flatten[Position[u, 1]] (* A219095 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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