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Template:Sequence of the Day for September 25

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Intended for: September 25, 2012

Timetable

  • First draft entered by Alonso del Arte on September 18, 2012
  • Draft reviewed by Daniel Forgues on September 24, 2012
  • Draft to be approved by August 25, 2012
Yesterday's SOTD * Tomorrow's SOTD

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A002064: Cullen numbers
Cn = n  2n + 1, n   ≥   0.
{ 1, 3, 9, 25, 65, 161, 385, 897, ... }
Grau proved that that there is no Cullen number with the Lehmer property. Hence, if
φ (Cn ) ∣ (Cn  −  1)
, then
Cn
is prime. A composite integer
m
is called a Lehmer number if
φ (m) ∣ (m  −  1)
, where
φ (m)
is the totient function.