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Date: 16-5-2020
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Date: 27-10-2019
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Date: 4-5-2020
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Let be a positive number, and define
(1) |
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(2) |
where the sum extends over the divisors of , and is the Möbius function. Then
(3) |
(Nagell 1951, p. 286).
For , 2, ..., is given by 0, 1, 3, 7, 11, 15, 20, 25, ... (OEIS A109507), where is the nearest integer function
REFERENCES:
Apostol, T. M. Introduction to Analytic Number Theory. New York: Springer-Verlag, 1976.
Nagell, T. "Further Lemmata. Proofs of Selberg's Formula." §73 in Introduction to Number Theory. New York: Wiley, pp. 279-280 and 283-286, 1951.
Selberg, A. "An Elementary Proof of the Prime Number Theorem." Ann. Math. 50, 305-313, 1949.
Sloane, N. J. A. Sequence A109507 in "The On-Line Encyclopedia of Integer Sequences."
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