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A373155
a(n) = 1 if n is a non-multiple of 3 whose 2-adic valuation is even, otherwise 0.
2
1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1
OFFSET
1
FORMULA
Multiplicative with a(2^e) = 1 if e is even, 0 if e is odd, a(3^e) = 0, and a(p^e) = 1 for any prime p > 3.
a(n) = A011655(n) * A035263(n).
a(n) = abs(A084091(n)) = A084091(n) mod 2.
From Amiram Eldar, May 29 2024: (Start)
Dirichlet g.f.: (2^s/(2^s+1)) * (1-1/3^s) * zeta(s).
Sum_{k=1..n} a(k) ~ (4/9) * n. (End)
MATHEMATICA
a[n_] := If[EvenQ[IntegerExponent[n, 2]] && !Divisible[n, 3], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)
PROG
(PARI) A373155(n) = ((n%3) && !(valuation(n, 2)%2));
(PARI) A373155(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !(f[k, 2]%2), f[k, 1] > 3)); };
CROSSREFS
Characteristic function of A084087.
Absolute values and also parity of A084091.
Sequence in context: A355328 A285258 A068428 * A078650 A285305 A372574
KEYWORD
nonn,mult,easy
AUTHOR
Antti Karttunen, May 28 2024
STATUS
approved