The On-Line Encyclopedia of Integer Sequences (OEIS)

A354199 revision #13

A354199

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.

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

FORMULA

a(n) = [A002654(n) == 1] = [A004018(n) == 4], where [ ] is the Iverson bracket.

a(n) = A053866(n) * (1-A353814(n)).

MATHEMATICA

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 *)

PROG

(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.

CROSSREFS

Characteristic function of A125853.

Cf. A002144, A002145, A002654, A004018, A053866.

Cf. also A353813, A353814.

Sequence in context: A297054 A359349 A266459 * A214509 A053866 A143259

Adjacent sequences: A354196 A354197 A354198 * A354200 A354201 A354202

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 25 2022

STATUS

approved