A359836 Parity of A353418, where A353418 is Dirichlet inverse of the characteristic function for numbers k where A156552(k) is a multiple of 3.

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 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, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = A353418(n) mod 2.

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

a(n) <= A359835(n).

a(n) <= A353269(n). [Conjectured. Note that as A329609 is not a multiplicative semigroup, the proof cannot be similar to that given in A353348 for A359826. See also A359835]

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));
memoA353418 = Map();
A353418(n) = if(1==n, 1, my(v); if(mapisdefined(memoA353418, n, &v), v, v = -sumdiv(n, d, if(d<n, A353269(n/d)*A353418(d), 0)); mapput(memoA353418, n, v); (v)));
A359836(n) = (A353418(n)%2);

Crossrefs

Cf. A003961, A156552, A348717, A353269, A353418, A359835.

Cf. also A353348 and A359826.

Sequence in context: A368997 A330682 A230135 * A359835 A353331 A353269

Adjacent sequences: A359833 A359834 A359835 * A359837 A359838 A359839

Keyword

nonn

Author

Antti Karttunen, Jan 17 2023

Status

approved