A353269 - OEIS

%I #22 Apr 16 2022 09:40:32

%S 1,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,1,

%T 0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0,1,0,0,1

%N a(n) = 1 if A156552(n) is a multiple of 3, otherwise 0.

%H Antti Karttunen, <a href="/A353269/b353269.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = 1 iff A329903(n) = 0, or equally, iff A332814(n) = 0.

%F a(n) = 1 iff A329903(2*n) = 1.

%F For n > 1, a(n) = 1 iff A341353(n) > 0.

%F a(n) >= A010052(n), for all n >= 1.

%F a(p) = 0 for all primes p.

%F a(2*A329604(n)) = 1, for all n >= 1.

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

%F a(n) = A353350(A332461(n)) = A353350(A332462(n)). - _Antti Karttunen_, Apr 15 2022

%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));

%Y Characteristic function of A329609. See also A332449, A353350, A353307 (bisection).

%Y Cf. A003961, A010052, A156552, A329604, A329903, A332461, A332462, A332814, A341353, A348717, A353303, A353362 (inverse Möbius transform).

%K nonn

%O 1

%A _Antti Karttunen_, Apr 10 2022