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**
How to Differentiate a Number
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Victor Ufnarovski

Centre for Mathematical Sciences

Lund Institute of Technology

P.O. Box 118

SE-221 00 Lund

Sweden

Bo Åhlander

KTH/2IT

Electrum 213

164 40 Kista

Sweden

**Abstract:**

We define the derivative of an integer to be the map sending every prime to 1 and
satisfying the Leibnitz rule.
The aim of the article is to consider the basic properties of this map
and to show how to generalize the notion to the case of rational and arbitrary real
numbers.
We make some conjectures and find some connections with
Goldbach's Conjecture and the Twin Prime Conjecture.
Finally, we
solve the easiest associated differential equations and calculate the generating function.

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(Concerned with sequence
A003415
.)

Received April 4, 2003;
revised version received July 27, 2003.
Published in *Journal of Integer Sequences*
September 17, 2003.

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