A353269 a(n) = 1 if A156552(n) is a multiple of 3, otherwise 0.

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, 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, 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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

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

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

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

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

a(p) = 0 for all primes p.

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

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

a(n) = A353350(A332461(n)) = A353350(A332462(n)). - Antti Karttunen, Apr 15 2022

Prog

(PARI)
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 };
A353269(n) = (!(A156552(n)%3));

Crossrefs

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

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

Sequence in context: A359836 A359835 A353331 * A205633 A352594 A252488

Adjacent sequences: A353266 A353267 A353268 * A353270 A353271 A353272

Keyword

nonn

Author

Antti Karttunen, Apr 10 2022

Status

approved