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A353269
a(n) = 1 if A156552(n) is a multiple of 3, otherwise 0.
16
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 10 2022
STATUS
approved