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Template:Sequence of the Day for September 13

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Intended for: September 13, 2011

Timetable

  • First draft entered by Charles R Greathouse IV on July 13, 2011
  • Draft reviewed by Alonso del Arte on July 13, 2011
  • Draft approved by Alonso del Arte on August 11, 2011
Yesterday's SOTD * Tomorrow's SOTD

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A070243:
Card{ k | φ (k)   ≤   n }, n   ≥   1
.
{ 2, 5, 5, 9, 9, 13, 13, 18, 18, 20, 20, 26, 26, 26, 26, 32, 32, 36, 36, 41, 41, 43, 43, 53, ... }
This sequence counts the number of positive integers
k
such that
φ (k)   ≤   n
, where
φ (k)
is Euler’s totient function. It has natural density
ζ  (2) ζ  (3)
ζ  (6 )
  ≈   1.9435
, so in some sense the values of
φ (k)
are on average not much less than
k
. Note that
a (n)  −  a (n  −  1) = Card{ k | φ (k) = n }, n   ≥   1,
(see A014197) and thus
a (n) =
n

m  = 1
A014197(m)
.