A336909 Numbers k > 2 such that omega(k) > log(log(k)) + sqrt(log(log(k))), where omega(k) is the number of distinct primes dividing k (A001221).

3, 4, 6, 10, 12, 14, 15, 30, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 195, 198, 204, 210, 220, 222, 228, 230, 231, 234, 330, 390, 420, 462, 510, 546, 570, 630, 660, 690

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 = 1, and therefore the asymptotic density of this sequence is erfc(1/sqrt(2))/2 = 0.158655... (A239382).

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, 700], PrimeNu[#] > Log[Log[#]] + Sqrt[Log[Log[#]]] &]

Crossrefs

Cf. A001221, A239382, A336910.

Sequence in context: A137951 A082694 A004793 * A031132 A322165 A057477

Adjacent sequences: A336906 A336907 A336908 * A336910 A336911 A336912

Keyword

nonn

Author

Amiram Eldar, Aug 07 2020

Status

approved