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Let sigma_infty(n) be the sum of the infinitary divisors of a number n. An infinitary perfect number is a number n such that sigma_infty(n)=2n. The first few are 6, 60, 90, ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

The exponent of the largest power of 2 which divides a given number 2n. The values of the ruler function for n=1, 2, ..., are 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, ... (OEIS A001511).

The signed Stirling numbers of the first kind are variously denoted s(n,m) (Riordan 1980, Roman 1984), S_n^((m)) (Fort 1948, Abramowitz and Stegun 1972), S_n^m (Jordan 1950). ...

A triangle-free graph is a graph containing no graph cycles of length three. A simple graph is triangle-free iff Tr(A^3)=0, where A is the adjacency matrix of the graph and ...

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...

The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as ...