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A373597
Non-multiples of 3 whose multiplicies of prime factors of types 3m-1 and 3m+1 are both multiples of 3.
9
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
1,2
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.
LINKS
EXAMPLE
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.
PROG
(PARI) isA373597 = A373596;
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).
Sequence in context: A308904 A192753 A373492 * A373589 A121307 A338471
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 10 2024
STATUS
approved