|
%I #13 May 17 2022 17:50:35
%S 0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T 1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,
%U 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1
%N a(n) = 1 if n is odd and sigma(n^2) == 3 (mod 4), otherwise 0.
%H Antti Karttunen, <a href="/A354035/b354035.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A000035(n) * A000035(A083025(n)).
%F a(n) = A000035(n) * [A010873(A065764(n)) == 3], where [ ] is the Iverson bracket.
%F a(n) = A000035(n) - A354036(n).
%t a[n_] := If[OddQ[n] && Mod[DivisorSigma[1, n^2], 4] == 3, 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 16 2022 *)
%o (PARI) A354035(n) = ((n%2)&&3==(sigma(n*n)%4));
%Y Characteristic function of A324909.
%Y Cf. A000035, A000203, A010873, A065764, A083025, A354036.
%K nonn
%O 1
%A _Antti Karttunen_, May 16 2022
|
