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The O'Nan group is the sporadic group O'N of order |O'N| = 460815505920 (1) = 2^9·3^4·5·7^3·11·19·31. (2) It is implemented in the Wolfram Language as ONanGroupON[].

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

The reciprocity theorem for x^8=q (mod p).

An odd chordless cycle is a chordless cycle of length >4. A graph is said to be perfect iff neither the graph G nor its graph complement G^_ has an odd chordless cycle. A ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

The odd part Od(n) of a positive integer n is defined by Od(n)=n/(2^(b(n))), where b(n) is the exponent of the exact power of 2 dividing n. Od(n) is therefore the product of ...

Any prime number other than 2 (which is the unique even prime). Humorously, 2 is therefore the "oddest" prime.

A graph vertex in a graph is said to be an odd node if its vertex degree is odd.

A set of maximum degree to which all other degrees of recursively enumerable sets can be one-one reduced. If set A is many-one complete, then it is one-one complete, and vice ...

A right or left ideal of a ring. The term is used especially in noncommutative rings to denote a right ideal that is not a left ideal, or conversely.