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

1,4

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A055188 A164885 A084989 * A115588 A240471 A263569

Adjacent sequences: A128535 A128536 A128537 * A128539 A128540 A128541

Keyword

easy,nonn

Author

Jonathan Vos Post, May 07 2007

Extensions

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

Status

approved