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A number n that has more divisors than any x < n is a highly composite number (though the first two such numbers are 1 and 2). Composite numbers have also been called "rectangular numbers", but that name can also refer to the pronic numbers, numbers that are the product of two consecutive integers.
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form (+). [1] The study of these numbers dates back to Aristotle.They are also called oblong numbers, heteromecic numbers, [2] or rectangular numbers; [3] however, the term "rectangular number" has also been applied to the composite numbers.
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
Picture Pages is a 1978–1984 American educational television program aimed at preschool children, presented by Bill Cosby—teaching lessons on basic arithmetic, geometry, word association and drawing through a series of interactive lessons that used a workbook that viewers would follow along with the lesson.
Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.
Tree showing all happy numbers up to 100, with 130 seen with 13 and 31 In number theory , a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1 2 + 3 2 = 10 {\displaystyle 1^{2}+3^{2}=10} , and 1 2 + 0 2 = 1 {\displaystyle 1^{2}+0^{2}=1} .
The nth pentagonal number p n is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of ...