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%I #11 May 17 2022 17:50:39
%S 1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,
%T 0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,
%U 1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N a(n) = 1 if n is odd and sigma(n^2) == 1 (mod 4), otherwise 0.
%H Antti Karttunen, <a href="/A354036/b354036.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) * [A010873(A065764(n)) == 1], where [ ] is the Iverson bracket.
%F a(n) = A000035(n) - A354035(n).
%t a[n_] := If[OddQ[n] && Mod[DivisorSigma[1, n^2], 4] == 1, 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 16 2022 *)
%o (PARI) A354036(n) = ((n%2)&&1==(sigma(n*n)%4));
%Y Characteristic function of A354039.
%Y Cf. A000035, A000203, A010873, A065764, A083025, A354035.
%K nonn
%O 1
%A _Antti Karttunen_, May 16 2022