In number theory, a k-hyperperfect number is a natural number n for which the equality n = 1 + k ( σ ( n ) − n − 1 ) {\displaystyle n=1+k(\sigma (n)-n-1)}...

odd-factor hyperperfect number 1301 = centered square number, Honaker prime, number of trees with 13 unlabeled nodes 1302 = Mertens function zero, number of edges...

perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers. Hyperperfect number Leinster...

325 is the smallest (and only known) 3-hyperperfect number. Sloane, N. J. A. (ed.). "Sequence A034897 (Hyperperfect numbers: x such that x = 1 + k*(sigma(x)-x-1)...

Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers". Unsolved Problems in Number Theory (2nd ed.). New York: Springer-Verlag. pp. 16...

Quasiperfect number Almost perfect number Multiply perfect number Hyperperfect number Semiperfect number Primitive semiperfect number Unitary perfect number Weird...

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has...

In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon: 2-3 . These are one type of 2-dimensional figurate...

In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including...

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...

In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function σ(n)) is equal to 2n +...

In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A...

In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

In number theory, a deficient number or defective number is a positive integer n for which the sum of divisors of n is less than 2n. Equivalently, it...

month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive...

A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n ( n + 1 ) {\displaystyle n(n+1)} . The study...

In number theory, a Carmichael number is a composite number ⁠ n {\displaystyle n} ⁠ which in modular arithmetic satisfies the congruence relation: b n...

numbers Highly composite numbers Highly totient numbers Home primes Hyperperfect numbers Juggler sequence Kolakoski sequence Lucky numbers Lucas numbers...

A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are...

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...

In number theory, a Sierpiński number is an odd natural number k such that k × 2 n + 1 {\displaystyle k\times 2^{n}+1} is composite for all natural numbers...

In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition...

polygonal number a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r =...

recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into...

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

Cullen number is a member of the integer sequence C n = n ⋅ 2 n + 1 {\displaystyle C_{n}=n\cdot 2^{n}+1} (where n {\displaystyle n} is a natural number). Cullen...