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A373154
a(n) = 1 if 6*n is squarefree, otherwise 0.
1
1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0
OFFSET
1
FORMULA
Multiplicative with a(p^e) = 0 if p <= 3 or e >= 2, and 1 otherwise.
a(n) = A008966(A008588(n)) = A008966(n) * A354354(n).
a(n) = abs(A355688(n)) = A355688(n) mod 2.
From Amiram Eldar, May 29 2024: (Start)
Dirichlet g.f.: (2^s/(2^s+1)) * (3^s/(3^s+1)) * zeta(s)/zeta(2*s).
Sum_{k=1..n} a(k) ~ (3/Pi^2) * n. (End)
MATHEMATICA
a[n_] := If[SquareFreeQ[6*n], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)
PROG
(PARI) A373154(n) = issquarefree(6*n);
(PARI) A373154(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 2] < (2-(f[k, 1]<=3))); };
CROSSREFS
Characteristic function of A276378.
Absolute values and also parity of A355688.
Sequence in context: A267056 A089024 A355688 * A353488 A232991 A168553
KEYWORD
nonn,easy,mult
AUTHOR
Antti Karttunen, May 28 2024
STATUS
approved