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sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

The Sims graph is a distance-transitive graph on 352 vertices (Brouwer et al. 1989, p. 370).

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

An even number of the form 4n+2 (i.e., an integer which is divisible by 2 but not by 4). The first few for n=0, 1, 2, ... are 2, 6, 10, 14, 18, ... (OEIS A016825)

The Reidemeister move of type III.

An algorithm for computing an Egyptian fraction.

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...