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A089997
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a(n) = Floor[Exp[(Composite[n]-Sqrt[Composite[n]*CompositePi[n]])/(-CompositePi[n]+ Sqrt[Composite[n]*CompositePi[n]])]]
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0
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7, 11, 16, 8, 9, 7, 8, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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1,1
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COMMENTS
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Complementary function to the log type function of the primes and their distributions as the function of the composites and their distribution.
The result even as an exponential function seems to tend to an asymototic limit.
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LINKS
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MATHEMATICA
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(* manufacture the composite numbers as a function*) p[n_]=n!/Product[Prime[i], {i, 2, PrimePi[n]}] digits=200 a0=Table[p[n]/p[n-1], {n, 2, digits}] c=Delete[Delete[Union[a0], 1], 1] d=Dimensions[c][[1]] Composite[n_]=c[[n]] (* make the log equivalent function*) g[n_]=(Composite[n]-Sqrt[Composite[n]*CompositePi[n]])/(-CompositePi[n]+ Sqrt[Composite[n]*CompositePi[n]]) e=Table[Floor[Exp[g[n]]], {n, 1, d-1}]
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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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