A359467 a(n) = (A166486(n)+A353627(n)) mod 2.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1

Offset

1

Links

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

Index entries for characteristic functions.

Formula

a(n) = (A166486(n)+A355689(n)) mod 2 = (A353627(n)+A358839(n)) mod 2.

a(n) = A342419(n) mod 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/4 - 4/Pi^2 = 0.344715... . - Amiram Eldar, Jan 24 2023

Mathematica

a[n_] := Module[{e = IntegerExponent[n, 2], o}, o = n/2^e; sqf = SquareFreeQ[o]; If[(e > 1 && sqf) || (e < 2 && ! sqf), 1, 0]]; Array[a, 100] (* Amiram Eldar, Jan 24 2023 *)

Prog

(PARI) A359467(n) = (((!(n%4))&&issquarefree(n>>valuation(n, 2))) + ((n%4)&&!issquarefree(n)));
(PARI)
A166486(n) = !!(n%4);
A355689(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], (-1)^f[k, 2], -(1==f[k, 2]))); };
A359467(n) = ((A166486(n)+A355689(n))%2);

Crossrefs

Characteristic function of A359468, numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree.

Cf. A166486, A355689, A342419, A353627, A358839.

Differs from A359466 for the first time at n=225, where a(225) = 1, while A359466(225) = 0.

Differs from A359469 [= A353459(n) mod 2] for the first time at n=100. Here a(100) = 0.

Sequence in context: A345951 A345952 A359466 * A359469 A107078 A341613

Adjacent sequences: A359464 A359465 A359466 * A359468 A359469 A359470

Keyword

nonn

Author

Antti Karttunen, Jan 02 2023

Status

approved