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A359467
a(n) = (A166486(n)+A353627(n)) mod 2.
4
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
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2023
STATUS
approved