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A general formula giving the number of distinct ways of folding an m×n rectangular map is not known. A distinct folding is defined as a permutation of N=m×n numbered cells ...

Write the exact powers of 2 and 3 in sorted order as 1, 2, 3, 4, 8, 9, 16, 27, 32, ... (OEIS A006899), and let u_n be the nth term in the sequence. Then u_(n+1)-u_n tends to ...

Like the entire harmonic series, the harmonic series sum_(k=1)^infty1/(p_k)=infty (1) taken over all primes p_k also diverges, as first shown by Euler in 1737 (Nagell 1951, ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A prime power is a prime or integer power of a prime. A test for a number n being a prime is implemented in the Wolfram Language as PrimePowerQ[n]. The first few prime powers ...

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...

The number of ways of folding a strip of stamps has several possible variants. Considering only positions of the hinges for unlabeled stamps without regard to orientation of ...

The von Staudt-Clausen theorem, sometimes also known as the Staudt-Clausen theorem (Carlitz 1968), states that B_(2n)=A_n-sum_(p_k; (p_k-1)|2n)1/(p_k), (1) where B_(2n) is a ...