A121307 -id:A121307 - cp's OEIS frontend

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

Reinhard Zumkeller, Oct 19 2008

nonn

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

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

Cf. A001222, A010872, A373975 (characteristic function).
Subsequences: A000578, A014612, A046316, A121307, A373589, A373590, A373597, A373837.
Cf. also A028260, A214195, A297845.

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

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

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

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

A373589 Numbers whose number of prime factors (with multiplicity) is a multiple of 3, and all of them are of the type 3m-1 (in A003627).

Original entry on oeis.org

1, 8, 20, 44, 50, 64, 68, 92, 110, 116, 125, 160, 164, 170, 188, 212, 230, 236, 242, 275, 284, 290, 332, 352, 356, 374, 400, 404, 410, 425, 428, 452, 470, 506, 512, 524, 530, 544, 548, 575, 578, 590, 596, 605, 638, 668, 692, 710, 716, 725, 736, 764, 782, 788, 830, 880, 890, 902, 908, 928, 932, 935, 956, 986, 1000

Offset: 1

Antti Karttunen, Jun 10 2024

A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

			1 is a term since it has no prime factors, 0 is a multiple of 3, and "the empty set has every property". - _N. J. A. Sloane_, Dec 16 2024

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A001222, A003627, A121307 (subsequence), A373588 (characteristic function).
Intersection of A004612 and A145784.
Subsequence of A373597, which in turn is a subsequence of many other sequences.
Cf. also A373590.

Join[{1},Select[Range[1000],Mod[PrimeOmega[#],3]==0&&Union[Mod[FactorInteger[#][[;;,1]],3]]=={2}&]] (* Harvey P. Dale, Dec 16 2024 *)

PARI
```
isA373589 = A373588;
```

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula