A031879 -id:A031879 - cp's OEIS frontend

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

Jonathan Vos Post, May 07 2007

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.

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

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

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 *)

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

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

A139787 Semiprime lucky numbers.

Original entry on oeis.org

9, 15, 21, 25, 33, 49, 51, 69, 87, 93, 111, 115, 129, 133, 141, 159, 169, 201, 205, 219, 235, 237, 259, 267, 289, 303, 319, 321, 327, 339, 361, 391, 393, 415, 427, 451, 489, 511, 517, 519, 529, 535, 537, 553, 559, 579, 583, 591, 655, 679, 685, 699, 717

Offset: 1

Jonathan Vos Post, May 20 2008

Subset of A031879 Composite lucky numbers.

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

Cf. A000959, A001358, A031879.

A000959 INTERSECTION A001358.

Term 135 deleted by Giovanni Resta, Jun 20 2016

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions