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A353361 Number of divisors d of n for which A156552(d) is not a multiple of 3.

%I A353361 #7 Apr 18 2022 17:48:53
%S A353361 0,1,1,1,1,3,1,2,1,2,1,4,1,3,3,2,1,4,1,3,2,2,1,6,1,3,2,4,1,5,1,3,3,2,
%T A353361 3,5,1,3,2,4,1,6,1,3,4,2,1,7,1,3,3,4,1,6,2,6,2,3,1,8,1,2,3,3,3,5,1,3,
%U A353361 3,6,1,8,1,3,4,4,3,6,1,5,2,2,1,8,2,3,2,4,1,7,2,3,3,2,3,9,1,4,4,4,1,5,1,6,5
%N A353361 Number of divisors d of n for which A156552(d) is not a multiple of 3.
%H A353361 Antti Karttunen, <a href="/A353361/b353361.txt">Table of n, a(n) for n = 1..65537</a>
%H A353361 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353361 a(n) = Sum_{d|n} (1-A353269(d)).
%F A353361 a(n) = A000005(n) - A353362(n).
%F A353361 a(p) = 1 for all primes p.
%F A353361 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%o A353361 (PARI)
%o A353361 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353361 A353269(n) = (!(A156552(n)%3));
%o A353361 A353361(n) = sumdiv(n,d,!A353269(d));
%Y A353361 Cf. A000005, A003961, A156552, A348717, A353269, A353350, A353362.
%Y A353361 Cf. also A353351.
%K A353361 nonn
%O A353361 1,6
%A A353361 _Antti Karttunen_, Apr 15 2022