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 Multiply...

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)...

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

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...

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...

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 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...

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...

A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are...

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 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...

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

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose...

mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer...

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...

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...

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...

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

In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus...

In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 ⋅ 2 n − 1 {\displaystyle 3\cdot 2^{n}-1} for a non-negative...

In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance...

In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer...

number theory, a Woodall number (Wn) is any natural number of the form W n = n ⋅ 2 n − 1 {\displaystyle W_{n}=n\cdot 2^{n}-1} for some natural number...

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...

k-gonal number contains k more dots than the previous layer. Each centered k-gonal number in the series is k times the previous triangular number, plus...

In mathematics, a Riesel number is an odd natural number k for which k × 2 n − 1 {\displaystyle k\times 2^{n}-1} is composite for all natural numbers...

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 mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function σ ( n ) {\displaystyle...