A128538 Number of prime factors (with multiplicity) of lucky numbers.

0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 3, 1, 2, 2, 3, 3, 2, 2, 1, 2, 2, 4, 2, 1, 2, 1, 2, 3, 4, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 1, 2, 3, 2, 3, 1, 3, 2, 4, 2, 1, 2, 2, 2, 1, 2, 1, 3, 2, 1, 3, 2, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 3, 3, 3, 1, 2, 4, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 3, 1, 4, 1, 3

Offset: 1

Author

Jonathan Vos Post, May 07 2007

Keywords

• easy
• nonn

Comments

a(n) = 0 iff n = 1. a(n) = 1 iff n-th lucky number is prime iff A000959(n) is in A031157 Numbers that are both lucky and prime. a(n) > 1 iff n-th lucky number is composite iff A000959(n) is in A031879 Composite lucky numbers [technically, A031879 should not begin with 1]. a(n) = 2 iff n-th lucky number is semiprime iff A000959(n) is in A001358. a(n) = 3 iff n-th lucky number has 3 prime factors (with multiplicity) iff A000959(n) is in A014612.

Links

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

Crossrefs

Cf. A000040, A000959, A001222, A001358, A014612, A031157, A031879.

Programs

Mathematica

L = Table[2*i + 1, {i, 0,400}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];PrimeOmega/@L (* James C. McMahon, Jan 09 2025 *)

Formula

a(n) = A001222(A000959(n)).

Extensions

More terms from R. J. Mathar, Oct 22 2010