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Computation of the Totient Summatory Function

math.NT · 2025-06-09 · conditional · novelty 6.0

A modified Dirichlet-hyperbola algorithm computes Φ(n) in Θ(n^{2/3}(ln ln n)^{1/3}) time and Θ(n^{1/3}(ln ln n)^{2/3}) space, and produced the first computation of Φ(10^19).

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  • Computation of the Totient Summatory Function math.NT · 2025-06-09 · conditional · none · ref 2

    A modified Dirichlet-hyperbola algorithm computes Φ(n) in Θ(n^{2/3}(ln ln n)^{1/3}) time and Θ(n^{1/3}(ln ln n)^{2/3}) space, and produced the first computation of Φ(10^19).