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Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...

Given a property P, if P(x)∼x as x->infty (so, using asymptotic notation, the number of numbers less than x not satisfying the property P is o(x), where o(x) is one of the ...

A number N=p_1p_2...p_n where the p_is are distinct primes and n>=3 such that p_i=Ap_(i-1)+B (1) for i=1, 2, ..., n, p_0 taken as 1, and with A and B some fixed integers. For ...

Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The ...

The number 13.

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

A modification of Legendre's formula for the prime counting function pi(x). It starts with |_x_| = (1) where |_x_| is the floor function, P_2(x,a) is the number of integers ...