Template:Sequence of the Day for September 25

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  2 n + 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.