A353380 a(n) = 1 if A353354(n) [= Sum_{d|n} A332823(d)] is zero, otherwise 0.

1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 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) = [A353328(n) = A353329(n)], where [ ] is the Iverson bracket, giving 1 only if A353328(n) and A353329(n) are equal, and 0 otherwise.

a(p) = 0 for all primes p.

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

Prog

(PARI)
A332823(n) = { my(f = factor(n), u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u, -1, u); };
A353354(n) = sumdiv(n, d, A332823(d));
A353380(n) = (0==A353354(n));

Crossrefs

Characteristic function of A353355.

Cf. A048675, A332823, A353328, A353329, A353354, A353381, A353382 (inverse Möbius transform), A353414.

Sequence in context: A266672 A266070 A262855 * A204171 A267612 A242252

Adjacent sequences: A353377 A353378 A353379 * A353381 A353382 A353383

Keyword

nonn

Author

Antti Karttunen, Apr 16 2022

Status

approved