Computing Prime Harmonic SumsMathematics of Computation
AbstractWe discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.
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Citation InformationE. Bach, D. Klyve, and J. Sorenson, Computing Prime Harmonic Sums, Mathematics of Computation 78:2283-2305, 2009.