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Numbers with property that the number of prime factors is a multiple of 3.
12

%I #22 Jul 02 2024 08:21:30

%S 1,8,12,18,20,27,28,30,42,44,45,50,52,63,64,66,68,70,75,76,78,92,96,

%T 98,99,102,105,110,114,116,117,124,125,130,138,144,147,148,153,154,

%U 160,164,165,170,171,172,174,175,182,186,188,190,195,207,212,216,222

%N Numbers with property that the number of prime factors is a multiple of 3.

%C A multiplicative semigroup: if m and n are in the sequence, then so is m*n. - _Antti Karttunen_, Jul 02 2024

%H Reinhard Zumkeller, <a href="/A145784/b145784.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (Haskell)

%o a145784 n = a145784_list !! (n-1)

%o a145784_list = filter ((== 0) . a010872 . a001222) [1..]

%o -- _Reinhard Zumkeller_, May 26 2012

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

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

%Y Cf. also A028260, A214195, A297845.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Oct 19 2008