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A353362 Number of divisors d of n for which A156552(d) is a multiple of 3.

%I A353362 #9 Apr 18 2022 17:48:58
%S A353362 1,1,1,2,1,1,1,2,2,2,1,2,1,1,1,3,1,2,1,3,2,2,1,2,2,1,2,2,1,3,1,3,1,2,
%T A353362 1,4,1,1,2,4,1,2,1,3,2,2,1,3,2,3,1,2,1,2,2,2,2,1,1,4,1,2,3,4,1,3,1,3,
%U A353362 1,2,1,4,1,1,2,2,1,2,1,5,3,2,1,4,2,1,2,4,1,5,2,3,1,2,1,3,1,2,2,5,1,3,1,2,3
%N A353362 Number of divisors d of n for which A156552(d) is a multiple of 3.
%H A353362 Antti Karttunen, <a href="/A353362/b353362.txt">Table of n, a(n) for n = 1..65537</a>
%H A353362 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353362 a(n) = Sum_{d|n} A353269(d).
%F A353362 a(n) = A000005(n) - A353361(n).
%F A353362 a(p) = 1 for all primes p.
%F A353362 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%o A353362 (PARI)
%o A353362 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 A353362 A353269(n) = (!(A156552(n)%3));
%o A353362 A353362(n) = sumdiv(n,d,A353269(d));
%Y A353362 Inverse Möbius transform of A353269.
%Y A353362 Cf. A000005, A003961, A156552, A348717, A353303, A353304, A353361.
%Y A353362 Cf. also A353352.
%Y A353362 Differs from A353332 for the first time at n=30, where a(30) = 3, while A353332(30) = 2.
%K A353362 nonn
%O A353362 1,4
%A A353362 _Antti Karttunen_, Apr 15 2022