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A342476
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Numbers m > 1 such that W(m) > W(k) for all 1 < k < m, where W(k) = omega(k)*log(log(k))/log(k).
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0
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2, 3, 4, 5, 6, 10, 12, 14, 15, 30, 210, 2310, 30030, 510510, 9699690, 223092870
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OFFSET
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1,1
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COMMENTS
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Includes the primorials prime(k)# = A002110(k) for 1 <= k <= 9.
Since the maximum of the function f(x) = log(log(x))/log(x) occurs at exp(e) = 15.154... (A073226), 15 is the largest term that is not a primorial.
The corresponding record values are -0.528..., 0.085..., 0.235..., 0.295..., 0.650..., 0.724..., 0.732..., 0.735..., 0.735..., 1.079..., 1.254..., 1.321..., 1.357..., 1.371..., 1.381..., 1.384...
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter V, p. 168.
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LINKS
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MATHEMATICA
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w[n_] := PrimeNu[n]*Log[Log[n]]/Log[n]; wmax = -1; seq = {}; Do[w1 = w[n]; If[w1 > wmax, wmax = w1; AppendTo[seq, n]], {n, 2, 2500}]; seq
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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