OFFSET
1,1
COMMENTS
According to Erdős-Kac theorem, the asymptotic density of the sequence of numbers k such that omega(k) > log(log(k)) + c * sqrt(log(log(k))), for all real numbers c, is erfc(c/sqrt(2))/2. Here c = 2, and therefore the asymptotic density of this sequence is erfc(sqrt(2))/2 = 0.022750... (A239383).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős and Mark Kac, The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions, American Journal of Mathematics, Vol. 62, No. 1 (1940), pp. 738-742, alternative link.
Mark Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Monograph 12, Math. Assoc. Amer., 1959, p. 75.
Alfréd Rényi and Pál Turán, On a theorem of Erdős-Kac, Acta Arithmetica, Vol. 4, No. 1 (1958), pp. 71-84.
Eric Weisstein's World of Mathematics, Erdős-Kac theorem.
Eric Weisstein's World of Mathematics, Erfc.
Wikipedia, Erdős-Kac theorem.
MATHEMATICA
Select[Range[3, 10^5], PrimeNu[#] > Log[Log[#]] + 2 * Sqrt[Log[Log[#]]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 07 2020
STATUS
approved