cp's OEIS Frontend

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

%I A373597 #23 Oct 06 2024 12:24:11
%S A373597 1,8,20,44,50,64,68,92,110,116,125,160,164,170,188,212,230,236,242,
%T A373597 275,284,290,332,343,352,356,374,400,404,410,425,428,452,470,506,512,
%U A373597 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
%N A373597 Non-multiples of 3 whose multiplicies of prime factors of types 3m-1 and 3m+1 are both multiples of 3.
%C A373597 A multiplicative semigroup: if m and n are in the sequence, then so is m*n. This is generated by semigroups A373589 and A373590.
%H A373597 Antti Karttunen, <a href="/A373597/b373597.txt">Table of n, a(n) for n = 1..20000</a>
%e A373597 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.
%e A373597 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.
%o A373597 (PARI) isA373597 = A373596;
%Y A373597 Cf. A002476, A003627, A373596 (characteristic function).
%Y A373597 Subsequences: A373589 and A373590.
%Y A373597 Subsequence of A001651, and of A145784.
%Y A373597 Subsequence of the sequences A369659, A369644, A327863, A289142, A373385, and some of their intersections: A373473, A373475, A373478, A373492, A373494.
%Y A373597 Differs from A373492 for the first time at n=91, where a(91) = 1325, which skips the value A373492(91) = 1323 present in A373492.
%Y A373597 Cf. also A046337 (roughly analogous sequence for k=2, instead of k=3).
%K A373597 nonn
%O A373597 1,2
%A A373597 _Antti Karttunen_, Jun 10 2024