44 (forty-four) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 43 and preceding 45.

In mathematics

Forty-four is a

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

and

palindromic number 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 reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...

. It is the tenth 10-

happy number 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, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...

, and the fourth

octahedral number In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

. It is a square-prime of the form ''p''² × ''q'', and fourth of this form and of the form 2² × ''q'', where ''q'' is a higher prime. It is the first member of the first cluster of two square-primes; of the form ''p''² × ''q'', specifically 2² × 11 = 44 and 3² × 5 = 45. The next such cluster of two square-primes comprises 2² × 29 = 116, and 3² × 13 = 117. 44 has an

aliquot sum In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociabl ...

of 40, within an

aliquot sequence In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Def ...

of three composite numbers (44, 40, 50, 43, 1, 0) rooted in the prime 43-aliquot tree. Since the greatest prime factor of 44² + 1 = 1937 is 149 and thus more than 44 twice, 44 is a

Størmer number In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n for which the greatest prime factor of n^2+1 is greater than or equal to 2n. They are named after Carl Størmer. Sequence The first Størmer numbers belo ...

. Given

Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...

, φ(44) = 20 and φ(69) = 44. 44 is a

tribonacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci seq ...

, preceded by 7, 13, and 24, whose sum it equals. 44 is the number of

derangement In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of a ...

s of 5 items. There are only 44 kinds of

Schwarz triangle In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping, through reflections in its edges. They were classified in . These can be defined mor ...

s, aside from the infinite

dihedra A dihedron (pl. dihedra) is a type of polyhedron, made of two polygon faces which share the same set of ''n'' edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dih ...

l family of triangles (''p'' 2 2) with ''p'' = . There are 44 distinct

stellation In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific ...

s of the

truncated cube In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangle (geometry), triangular), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triak ...

and

truncated octahedron In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagon, hexagons and 6 Squa ...

, per Miller's rules. 44 four-dimensional crystallographic point groups of a total

227 Year 227 (Roman numerals, CCXXVII) was a common year starting on Monday of the Julian calendar. At the time, it was known as the Year of the Consulship of Senecio and Fulvius (or, less frequently, year 980 ''Ab urbe condita''). The denomination ...

contain dual

enantiomorphs In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be ...

, or mirror images. There are forty-four classes of

finite simple groups In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple gr ...

that arise from four general families of such groups: * Two general groups stem from

cyclic group In abstract algebra, a cyclic group or monogenous group is a Group (mathematics), group, denoted C_n (also frequently \Z_n or Z_n, not to be confused with the commutative ring of P-adic number, -adic numbers), that is Generating set of a group, ge ...

s and

alternating group In mathematics, an alternating group is the Group (mathematics), group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted ...

s. * Sixteen families of groups stem from

simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by John ...

groups of Lie type In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phra ...

. * Twenty-six groups are

sporadic The qualification sporadic, indicating that occurrences of some phenomenon are rare and not systematic, can be used for: Mathematics * Sporadic group, any of a small number of finite groups that do not fit into any infinite family of groups Medic ...

. Sometimes the

Tits group In group theory, the Tits group 2''F''4(2)′, named for Jacques Tits (), is a finite simple group of order : 17,971,200 = 211 · 33 · 52 · 13. This is the only simple group that is a derivativ ...

is considered a 17th non-strict simple group of Lie type, or a 27th sporadic group, which would yield a total of 45 classes of finite simple groups.

In other fields

Forty-four is: *

Mark Twain Samuel Langhorne Clemens (November 30, 1835 – April 21, 1910), known by the pen name Mark Twain, was an American writer, humorist, and essayist. He was praised as the "greatest humorist the United States has produced," with William Fau ...

's ''

The Mysterious Stranger ''The Mysterious Stranger'' is a novella by the American author Mark Twain. He worked on it intermittently from 1897 through 1908. Twain wrote multiple versions of the story; each involves a supernatural character called "Satan" or "No. 44", enc ...

'' features

Satan Satan, also known as the Devil, is a devilish entity in Abrahamic religions who seduces humans into sin (or falsehood). In Judaism, Satan is seen as an agent subservient to God, typically regarded as a metaphor for the '' yetzer hara'', or ' ...

's supposed nephew, whose alternate name in parallel works is "44". * A song by The Residents. In "44", included in The Residents' ''Live at the Fillmore'' album, the number 44 is a main focus. * The international country code for

United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotlan ...

References

{{Integers, zero Integers