A353331 a(n) = 1 if A001222(n) [bigomega(n)] and A056239(n) are both even, otherwise a(n) = 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, 0, 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, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 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) = [A008836(n) = +1] * [A056239(n) = 0 (mod 2)], where [ ] is the Iverson bracket.

a(n^2) = 1 for all n.

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

Prog

(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
A353331(n) = ((!(bigomega(n)%2)) && (!(A056239(n)%2)));

Crossrefs

Characteristic function of A340784.

Cf. A000290, A001222, A003961, A008836, A056239, A348717, A353332 (inverse Möbius transform), A353333, A353334.

Differs from A353269 for the first time at n=30.

Sequence in context: A230135 A359836 A359835 * A353269 A205633 A352594

Adjacent sequences: A353328 A353329 A353330 * A353332 A353333 A353334

Keyword

nonn

Author

Antti Karttunen, Apr 14 2022

Status

approved