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Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

1. A fixed polyomino. 2. The set of points obtained by taking the centers of a fixed polyomino.

The 4-polyhex illustrated above (Gardner 1978, p. 147).

A polyhex consisting of hexagons arranged along a line.

A polyiamond consisting of equilateral triangles arranged along a line.

The 4-polyhex illustrated above.

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

The 6-polyiamond illustrated above.