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A354199
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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.
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2
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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, 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, 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
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OFFSET
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1
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LINKS
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FORMULA
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a(n) = [A002654(n) == 1] = [A004018(n) == 4], where [ ] is the Iverson bracket.
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MATHEMATICA
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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 *)
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PROG
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(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); };
(PARI) A354199(n) = (1==sumdiv( n, d, (d%4==1) - (d%4==3)));
(PARI) A354199(n) = ((issquare(n) || issquare(2*n)) && !A353814(n)); \\ Uses the program given in A353814.
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CROSSREFS
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Characteristic function of A125853.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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