About your reason for asking. See https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.nmj/1306851587 or the arxiv version https://arxiv.org/pdf/0906.1029.pdf where such things are discussed. In particular, the partial sums $\sum_{n\leq x}\exp(2\pi i\Omega(n)/k)$ are not $o(x^\alpha)$ for any $\alpha<1$.
Michael Coons
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