OFFSET
1,2
COMMENTS
This is a subsequence of A373475, containing all its terms that are not multiples of 3. (See comments in A373475 for a proof). The first difference from A373475 is at n=4186, where A373475(4186) = 19683 = 3^9, the value which is missing from this sequence. - Antti Karttunen, Jun 07 2024
From Antti Karttunen, Jun 11 2024: (Start)
A multiplicative semigroup: if m and n are in the sequence, then so is m*n.
Numbers that are not multiples of 3, and the multiplicities of prime factors of the forms 3m+1 (A002476) and 3m-1 (A003627) are equal modulo 3.
Like A373597, which is a subsequence, also this sequence can be viewed as a kind of k=3 variant of A046337.
A289142, numbers whose sum of prime factors (with multiplicity, A001414) is a multiple of 3, is generated (as a multiplicative semigroup) by the union of this sequence with {3}.
A327863, numbers whose arithmetic derivative is a multiple of 3, is generated by this sequence and A008591.
A373478, numbers that are in the intersection of A289142 and A327863, is generated by the union of this sequence with {9, 27}.
A373475, numbers that are in the intersection of A289142 and A369644 (positions of multiples of 3 in A083345), is generated by the union of this sequence with {19683}, where 19683 = 3^9.
(End)
The integers in the multiplicative subgroup of positive rationals generated by semiprimes of the form 3m+2 (A344872) and cubes of primes except 27. - Peter Munn, Jun 19 2024
LINKS
EXAMPLE
280 = 2*2*2*5*7 is included as it is not a multiple of 3, and one of its prime factors (7) is of the form 3m+1 and four are of the form 3m-1, and because 4 == 1 (mod 3). Also, A001414(280) = 18, and A003415(280) = 516, both of which are multiples of 3. - Antti Karttunen, Jun 12 2024
PROG
(PARI) \\ See A369658.
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 10 2024
EXTENSIONS
Name amended with an alternative definition by Antti Karttunen, Jun 11 2024
STATUS
approved