A374053 Multiplicative with a(3^k) = 0, a(p^(2k)) = 0 and a(p^(2k+1)) = 1 if p == 1 (mod 3), and a(p^(2k)) = 1 and a(p^(2k+1)) = 0, if p == -1 (mod 3).

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

Offset

1

Comments

This differs from A070563 for the first time at n=2401.

Links

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

Index entries for characteristic functions.

Mathematica

f[p_, e_] := If[Mod[p, 3] == 1, Mod[e, 2], 1 - Mod[e, 2]]; f[3, e_] := 0; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 13 2025 *)

Prog

(PARI) A374053(n) = { my(f=factor(n)); prod(i=1, #f~, if(0==(f[i, 1]%3), 0, if(1==(f[i, 1]%3), f[i, 2]%2, (1+f[i, 2])%2))); };

Crossrefs

Cf. A070563, A353815.

Sequence in context: A014099 A037011 A070563 * A024692 A373604 A079978

Adjacent sequences: A374050 A374051 A374052 * A374054 A374055 A374056

Keyword

nonn,mult

Author

Antti Karttunen after Christian G. Bower's conjectured formula for A070563, Jul 03 2024

Status

approved