cp's OEIS Frontend

A353328 Number of divisors d of n for which A332823(d) is positive (+1).

%I A353328 #16 Apr 27 2022 13:54:56
%S A353328 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 A353328 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 A353328 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 A353328 Number of divisors d of n for which A332823(d) is positive (+1).
%C A353328 Number of divisors of n such that A048673(d) == +1 (mod 3).
%H A353328 Antti Karttunen, <a href="/A353328/b353328.txt">Table of n, a(n) for n = 1..65537</a>
%H A353328 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353328 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 A353328 a(n) = A353354(n) + A353329(n).
%F A353328 a(n) = A353351(n) - A353329(n).
%F A353328 a(n) = A353329(A003961(n)).
%o A353328 (PARI)
%o A353328 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 A353328(n) = sumdiv(n,d,(A332823(d)>0));
%Y A353328 Cf. A003961, A048675, A332823, A353329, A353351, A353352, A353354.
%Y A353328 Cf. A353355 [a(n) == A353329(n)], A353356 [a(n) > A353329(n)],  A353357 [a(n) < A353329(n)].
%K A353328 nonn
%O A353328 1,10
%A A353328 _Antti Karttunen_ and _Peter Munn_, Apr 16 2022