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A semiprime, also called a 2-almost prime, biprime (Conway et al. 2008), or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few ...

1729 is sometimes called the Hardy-Ramanujan number. It is the smallest taxicab number, i.e., the smallest number which can be expressed as the sum of two cubes in two ...

A number n for which the harmonic mean of the divisors of n, i.e., nd(n)/sigma(n), is an integer, where d(n)=sigma_0(n) is the number of positive integer divisors of n and ...

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 Lochs' ...

A polygonal number of the form n(3n-1)/2. The first few are 1, 5, 12, 22, 35, 51, 70, ... (OEIS A000326). The generating function for the pentagonal numbers is ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

Take any positive integer of two digits or more, reverse the digits, and add to the original number. This is the operation of the reverse-then-add sequence. Now repeat the ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

The complementary Bell numbers, also called the Uppuluri-Carpenter numbers, B^~_n=sum_(k=0)^n(-1)^kS(n,k) (1) where S(n,k) is a Stirling number of the second kind, are ...