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The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it ...