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%I #13 Jun 13 2024 16:52:22
%S 1,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,
%T 1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,0,1,
%U 0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,1
%N a(n) = 1 if the sum of prime factors with repetition is a multiple of 3, otherwise 0.
%C a(n) = 1 if the multiplicities of prime factors of the forms 3m+1 (A002476) and 3m-1 (A003627) are equal modulo 3, otherwise 0. - _Antti Karttunen_, Jun 13 2024
%H Antti Karttunen, <a href="/A373371/b373371.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [A001414(n) == 0 (mod 3)], where [ ] is the Iverson bracket.
%F From _Antti Karttunen_, Jun 13 2024: (Start)
%F a(n) = [A373591(n) == A373592(n) (mod 3)].
%F a(n) = a(n/A038500(n)) = A359430(n/A038500(n)) = A369658(n/A038500(n)).
%F (End)
%o (PARI)
%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373371(n) = !(A001414(n)%3);
%o (PARI) A373371(n) = { my(f = factor(n),m1=0,m2=0); for(i = 1, #f~, if(1==(f[i, 1]%3), m1 += f[i,2], if(2==(f[i, 1]%3), m2 += f[i,2]))); 0==((m1-m2)%3); }; \\ _Antti Karttunen_, Jun 13 2024
%Y Characteristic function of A289142.
%Y Cf. A001414, A002476, A003627, A038500, A373591, A373592.
%Y Cf. also A359430, A369658, A373372.
%K nonn,changed
%O 1
%A _Antti Karttunen_, Jun 02 2024
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