

A342476


Numbers m > 1 such that W(m) > W(k) for all 1 < k < m, where W(k) = omega(k)*log(log(k))/log(k).


0



2, 3, 4, 5, 6, 10, 12, 14, 15, 30, 210, 2310, 30030, 510510, 9699690, 223092870
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OFFSET

1,1


COMMENTS

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...


REFERENCES

József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter V, p. 168.


LINKS



MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



