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From Ridouane Oudra, Jun 02 2024: (Start)
a(n) = (-1)^A066829(n);
a(n) = (-1)^A063647(n);
a(n) = sin(tau(n^2)*Pi/2). (End)
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Coons and Borwein: "We give a new proof of Fatou's theorem: if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function. This result is applied to show that for any nontrivial non-trivial completely multiplicative function from N to {-1,1}, the series sum_{n=1..infinity} f(n)z^n is transcendental over {Z}[z]; in particular, sum_{n=1..infinity} lambda(n)z^n is transcendental, where lambda is Liouville's function. The transcendence of sum_{n=1..infinity} mu(n)z^n is also proved." - Jonathan Vos Post, Jun 11 2008
sign,easy,nice,mult,changed
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Coons and Borwein: "We give a new proof of Fatou's theorem: if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function. This result is applied to show that for any non-trivial nontrivial completely multiplicative function from N to {-1,1}, the series sum_{n=1..infinity} f(n)z^n is transcendental over {Z}[z]; in particular, sum_{n=1..infinity} lambda(n)z^n is transcendental, where lambda is Liouville's function. The transcendence of sum_{n=1..infinity} mu(n)z^n is also proved." - Jonathan Vos Post, Jun 11 2008
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