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For (1) see Landau’s “Handbuchder ....Primzahlen II”. (2), (3) and the conjecture (?) are due to Chowla and Pillai. SeeJourn. London Math. Soc., 1930,5, 95–101.
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Communicated by Dr. S. Chowla.
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Sarma, M.L.N. On the error term in a certain sum. Proc. Indian Acad. Sci. 3, 338 (1936). https://doi.org/10.1007/BF03046269
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DOI: https://doi.org/10.1007/BF03046269