A353361 - OEIS

%I #7 Apr 18 2022 17:48:53

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

%H Antti Karttunen, <a href="/A353361/b353361.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} (1-A353269(d)).

%F a(n) = A000005(n) - A353362(n).

%F a(p) = 1 for all primes p.

%F a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

%o (PARI)

%o 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 A353269(n) = (!(A156552(n)%3));

%o A353361(n) = sumdiv(n,d,!A353269(d));

%Y Cf. A000005, A003961, A156552, A348717, A353269, A353350, A353362.

%Y Cf. also A353351.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 15 2022