A343911 a(n) = Omega(phi(n)), where Omega is the number of prime factors of n with multiplicity and phi is the Euler totient function.

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 3, 4, 3, 4, 4, 4, 3, 3, 3, 4, 2, 2, 4, 3, 3, 5, 4, 3, 3, 4, 4, 4, 3, 2, 4, 4, 3, 4, 5, 5, 3, 3, 5, 3, 4, 3, 4, 5, 4, 4, 4, 4, 4, 3, 5, 4, 4, 2, 4, 6, 3, 4, 4, 4, 4, 5, 3, 4, 2

Offset

1,5

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Paul Erdős and Carl Pomerance, On the normal number of prime factors of phi(n), Rocky Mountain J. Math., Vol. 15, No. 2 (1985), pp. 343-352.

Formula

a(n) = A001222(A000010(n)).

Limit_{x -> oo} (1/x) * Card({n <= x, a(n) - (1/2)*log(log(x))^2 <= (u/sqrt(3))*log(log(x))^(3/2)}) = (1 + erf(u/sqrt(2)))/2, for every real number u (Erdős and Pomerance, 1985). - Amiram Eldar, Nov 16 2024

Mathematica

Table[PrimeOmega[EulerPhi[n]], {n, 100}]

Prog

(PARI) a(n) = bigomega(eulerphi(n)); \\ Amiram Eldar, Nov 16 2024

Crossrefs

Cf. A000010 (phi), A001222 (Omega).

Sequence in context: A339931 A339221 A025851 * A125688 A230257 A060508

Adjacent sequences: A343908 A343909 A343910 * A343912 A343913 A343914

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 03 2021

Status

approved