A354029 - OEIS

%I #19 Jan 09 2023 19:26:50

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A354029/b354029.txt">Table of n, a(n) for n = 1..65539</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

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

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

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

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

%o (PARI) A354029(n) = ((3==((n>>!(n%2))%4)) && isprimepower(n>>!(n%2)));

%o (PARI) A354029(n) = ((0==(sigma(n)%4)) && (2==((eulerphi(n)%4))));

%Y Characteristic function of A292762.

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

%K nonn

%O 1

%A _Antti Karttunen_, May 15 2022