A128538 - OEIS

%I #14 Jan 09 2025 20:38:53

%S 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,

%T 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,

%U 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

%N Number of prime factors (with multiplicity) of lucky numbers.

%C 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.

%H Amiram Eldar, <a href="/A128538/b128538.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

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

%K easy,nonn

%O 1,4

%A _Jonathan Vos Post_, May 07 2007

%E More terms from _R. J. Mathar_, Oct 22 2010