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Template:Sequence of the Day for June 21

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Intended for: June 21, 2013

Timetable

  • First draft entered by Daniel Forgues on June 21, 2016
  • Draft reviewed by April 21, 2013
  • Draft approved by May 21, 2013
Yesterday's SOTD * Tomorrow's SOTD

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A003415:
a (n) = n
, the arithmetic derivative of
n: a (0) = a (1) = 0, a ( prime) = 1, a (mn) = m  a (n) + n  a (m)
.
{ 0, 0, 1, 1, 4, 1, 5, 1, 12, 6, 7, 1, 16, ... }
Based on the product rule for differentiation of functions: for functions
f  (x)
and
g (x)
,
( fg ) = fg + fg
. So with numbers,
(ab) = ab + ab
. This implies
1 = 0
.