A373597 Non-multiples of 3 whose multiplicies of prime factors of types 3m-1 and 3m+1 are both multiples of 3.

1, 8, 20, 44, 50, 64, 68, 92, 110, 116, 125, 160, 164, 170, 188, 212, 230, 236, 242, 275, 284, 290, 332, 343, 352, 356, 374, 400, 404, 410, 425, 428, 452, 470, 506, 512, 524, 530, 544, 548, 575, 578, 590, 596, 605, 637, 638, 668, 692, 710, 716, 725, 736, 764, 782, 788, 830, 880, 890, 902, 908, 928, 931, 932, 935

Offset: 1

Author

Antti Karttunen, Jun 10 2024

Keywords

• nonn

Comments

A multiplicative semigroup: if m and n are in the sequence, then so is m*n. This is generated by semigroups A373589 and A373590.

Examples

			20 = 2*2*5 has 0 primes of type 3m+1 (A002476) and 3 primes of type 3m-1 (A003627) in its prime factorization, and as 0 and 3 are both multiples of 3, 20 is included as a term.
21952 = 2^6 * 7^3 is a term because there are 3 primes of type 3m+1 and 6 primes of type 3m-1, and as 6 and 3 are both multiples of 3, 21952 is included as a term.
		

Links

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

Crossrefs

Cf. A002476, A003627, A373596 (characteristic function).

Subsequences: A373589 and A373590.

Subsequence of A001651, and of A145784.

Subsequence of the sequences A369659, A369644, A327863, A289142, A373385, and some of their intersections: A373473, A373475, A373478, A373492, A373494.

Differs from A373492 for the first time at n=91, where a(91) = 1325, which skips the value A373492(91) = 1323 present in A373492.

Cf. also A046337 (roughly analogous sequence for k=2, instead of k=3).

Programs

PARI

isA373597 = A373596;