A145784 Numbers with property that their number of prime factors counted with multiplicity is a multiple of 3.

1, 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 64, 66, 68, 70, 75, 76, 78, 92, 96, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 144, 147, 148, 153, 154, 160, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 216, 222

Offset: 1

Author

Reinhard Zumkeller, Oct 19 2008

Keywords

• nonn

Comments

A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - Antti Karttunen, Jul 02 2024

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A010872, A373975 (characteristic function).

Subsequences: A000578, A014612, A046316, A121307, A373589, A373590, A373597, A373837.

Cf. also A028260, A214195, A297845.

Programs

Haskell

a145784 n = a145784_list !! (n-1)
a145784_list = filter ((== 0) . a010872 . a001222) [1..]
-- Reinhard Zumkeller, May 26 2012

Mathematica

Join[{1}, Select[Range[2,230], Mod[Total[Transpose[FactorInteger[#]][[2]]], 3] == 0 &]] (* T. D. Noe, May 21 2012 *)

PARI

isok(k) = !(bigomega(k) % 3); \\ Amiram Eldar, May 16 2025

Formula

A010872(A001222(a(n))) = 0.