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).

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

1,2

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(PARI) isA373589 = A373588;

Crossrefs

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.

Sequence in context: A192753 A373492 A373597 * A121307 A338471 A086169

Adjacent sequences: A373586 A373587 A373588 * A373590 A373591 A373592

Keyword

nonn,easy

Author

Antti Karttunen, Jun 10 2024

Status

approved