Geodesic
The Series Σ∞ 1 f(n)/n for Periodic f
Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 413-432

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We are here concerned with the problem of deciding when Σ∞ n=1 f(n)/n ≠ 0, given that f is periodic and the series convergent. In particular, we considerConjecture A. Let p be a positive integer and f a (real-or complex-valued) number-theoretic function with period p. 
Livingston, Arthur E. The Series Σ∞ 1 f(n)/n for Periodic f. Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 413-432. doi: 10.4153/CMB-1965-029-2
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