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%I #16 Apr 27 2022 13:54:56
%S 0,1,0,1,1,1,0,1,1,2,1,2,0,1,1,2,1,2,0,2,1,2,1,2,1,1,1,2,0,3,1,2,1,2,
%T 1,3,0,1,1,3,1,2,0,2,2,2,1,3,1,2,1,2,0,3,2,2,1,1,1,4,0,2,2,2,1,3,1,2,
%U 1,3,0,4,1,1,2,2,1,2,0,4,1,2,1,4,2,1,1,3,0,4,1,2,1,2,1,4,1,2,2,3,0,3,1,2,2
%N Number of divisors d of n for which A332823(d) is positive (+1).
%C Number of divisors of n such that A048673(d) == +1 (mod 3).
%H Antti Karttunen, <a href="/A353328/b353328.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = Sum_{d|n} [A332823(d) > 0], where [ ] is the Iverson bracket, giving 1 only if A332823 computed for the divisor d is strictly positive, and 0 otherwise.
%F a(n) = A353354(n) + A353329(n).
%F a(n) = A353351(n) - A353329(n).
%F a(n) = A353329(A003961(n)).
%o (PARI)
%o A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
%o A353328(n) = sumdiv(n,d,(A332823(d)>0));
%Y Cf. A003961, A048675, A332823, A353329, A353351, A353352, A353354.
%Y Cf. A353355 [a(n) == A353329(n)], A353356 [a(n) > A353329(n)], A353357 [a(n) < A353329(n)].
%K nonn
%O 1,10
%A _Antti Karttunen_ and _Peter Munn_, Apr 16 2022
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