Template:Sequence of the Day for June 21

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 (m n) = 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)

,

( f g )′ = f ′g + f g ′

. So with numbers,

(ab)′ = a′ b + a b′

. This implies

1′ = 0

.