A369975 Parity of A369974.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A369974(n) mod 2 = A369978(n) mod 2.

a(n) <= A369001(n). [Because A369002 is a multiplicative semigroup; proof is similar to one given in A359780.]

Prog

(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
memoA369974 = Map();
A369974(n) = if(1==n, 1, my(v); if(mapisdefined(memoA369974, n, &v), v, v = -sumdiv(n, d, if(d<n, A369001(n/d)*A369974(d), 0)); mapput(memoA369974, n, v); (v)));
A369975(n) = (A369974(n)%2);

Crossrefs

Characteristic function of A369976.

Parity of A369974 and of A369978.

Cf. A083345, A369002.

Differs from A369001 for the first time at n=81, where a(81) = 0, while A369001(81) = 1.

Cf. also A359780.

Sequence in context: A353557 A324917 A369974 * A369001 A361024 A354037

Adjacent sequences: A369972 A369973 A369974 * A369976 A369977 A369978

Keyword

nonn

Author

Antti Karttunen, Feb 09 2024

Status

approved