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%I #13 May 25 2022 22:51:26
%S 1,1,0,1,0,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T 0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%U 0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1
%N a(n) = 1 if in the prime factorization of n there is no prime factor of form 4k+1 and any prime factor of form 4k+3 occurs with an even multiplicity, otherwise 0.
%H Antti Karttunen, <a href="/A354199/b354199.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [A002654(n) == 1] = [A004018(n) == 4], where [ ] is the Iverson bracket.
%F a(n) = A053866(n) * (1-A353814(n)).
%t a[1] = 1; a[n_] := If[AllTrue[FactorInteger[n], First[#] == 2 || (Mod[First[#], 4] == 3 && EvenQ[Last[#]]) &], 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 25 2022 *)
%o (PARI) A354199(n) = { my(f=factor(n)); for(k=1,#f~,if((1==(f[k,1]%4)) || ((3==(f[k,1]%4))&&(f[k,2]%2)),return(0))); (1); };
%o (PARI) A354199(n) = (1==sumdiv( n, d, (d%4==1) - (d%4==3)));
%o (PARI) A354199(n) = ((issquare(n) || issquare(2*n)) && !A353814(n)); \\ Uses the program given in A353814.
%Y Characteristic function of A125853.
%Y Cf. A002144, A002145, A002654, A004018, A053866.
%Y Cf. also A353813, A353814.
%K nonn
%O 1
%A _Antti Karttunen_, May 25 2022
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