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I am looking for a category of natural numbers (about <1000 is enough) with its properties.

Here's some examples :

2 - It is the first prime number.

1729 - It is the smallest number expressible as the sum of two cubes in two different ways.

Here's some bad examples that I don't focus on :

36 - It is the number that its half is equal to multiplying each digits (3 and 6 in this case).

69 - It is the number which has a sexual meaning.

36 is the bad example because it depends on the base 10.

Is there any site about this?

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4 Answers

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Wikipedia article List of numbers links to articles about individual numbers. They have covered all natural numbers up to 1000, and some beyond that range.

I like the subheading of the article:

This is an incomplete list which may never be able to satisfy particular standards for completeness. You can help by expanding it ...

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I don't think "category" is quite what you mean, maybe "catalogue"? Anyway as a printed reference there's David Wells' Dictionary of Curious and Interesting Numbers and online, there are wiki entries for small integers, e.g. 37

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(for example). Please see thread

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A site that has some curiosities about natural numbers are but as any site that lists curiosities it will be incomplete but perhaps it satisfies your needs.

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