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(Python)
from sympy import factorint
def A008836(n): return -1 if sum(factorint(n).values()) % 2 else 1 # Chai Wah Wu, May 24 2022
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Michael Coons, <a href="http://arxiv.org/abs/0810.3709">(Non)Automaticity of number theoretic functions</a>, arXiv:0810.3709 [math.NT], Oct 21, 2008.
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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 completely multiplicative function from N to {-1,1), }, the series sum_{n=1 to ..infinity) } f(n)z^n is transcendental over {Z}[z]; in particular, sum_{n=1 to ..infinity) } lambda(n)z^n is transcendental, where lambda is Liouville's function. The transcendence of sum_{n=1 to ..infinity) } mu(n)z^n is also proved." - Jonathan Vos Post, Jun 11 2008
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