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A354029
a(n) = 1 if either n or n/2 is a prime power of the form 4m+3, otherwise 0.
3
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
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.
Sequence in context: A364251 A365421 A131378 * A189624 A014707 A288213
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 15 2022
STATUS
approved