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Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

The twin primes constant Pi_2 (sometimes also denoted C_2) is defined by Pi_2 = product_(p>2; p prime)[1-1/((p-1)^2)] (1) = product_(p>2; p prime)(p(p-2))/((p-1)^2) (2) = ...

The Erdős-Borwein constant E, sometimes also denoted alpha, is the sum of the reciprocals of the Mersenne numbers, E = sum_(n=1)^(infty)1/(2^n-1) (1) = ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then for ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

Van der Corput's constant is given by m = 2sqrt(2)int_0^(sqrt(pi/2-c))cos(x^2+c)dx (1) = 2pi[coscC(phi)-sincS(phi)] (2) = 3.3643175781... (3) (OEIS A143305), where C(x) and ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...