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Date: 3-6-2020
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Date: 1-12-2020
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Date: 22-11-2020
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The Dedekind -function is defined by the divisor product
(1) |
where the product is over the distinct prime factors of , with the special case . The first few values are
(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
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(11) |
giving 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, ... (OEIS A001615).
Sums for include
(12) |
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(13) |
where is the Möbius function.
The Dirichlet generating function is given by
(14) |
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(15) |
where is the Riemann zeta function.
REFERENCES:
Cox, D. A. Primes of the Form x2+ny2: Fermat, Class Field Theory and Complex Multiplication. New York: Wiley, p. 228, 1997.
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 96, 1994.
Sloane, N. J. A. Sequence A001615/M2315 in "The On-Line Encyclopedia of Integer Sequences."
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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