A354029 a(n) = 1 if either n or n/2 is a prime power of the form 4m+3, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65539

Index entries for characteristic functions

Formula

For odd n, a(n) = A354028(n), and for even n, a(n) = A354028(n/2).

a(n) = [A105824(n) == 0] * [A353768(n) == 2], where [ ] is the Iverson bracket.

a(n) = 1 iff sigma(n) == 0 mod 4 and phi(n) == 2 mod 4.

For n > 1, a(n) = A354032(n) - A353812(n).

Mathematica

Boole[Table[AnyTrue[{n, n/2}, PrimePowerQ]&&MemberQ[Mod[{n, n/2}, 4], 3], {n, 140}]] (* Harvey P. Dale, Jan 09 2023 *)

Prog

(PARI) A354029(n) = ((3==((n>>!(n%2))%4)) && isprimepower(n>>!(n%2)));
(PARI) A354029(n) = ((0==(sigma(n)%4)) && (2==((eulerphi(n)%4))));

Crossrefs

Characteristic function of A292762.

Cf. A000010, A000203, A010873, A105824, A353768, A353812, A354028, A354032.

Sequence in context: A364251 A365421 A131378 * A189624 A014707 A288213

Adjacent sequences: A354026 A354027 A354028 * A354030 A354031 A354032

Keyword

nonn

Author

Antti Karttunen, May 15 2022

Status

approved