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 ...
in
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 2
2 × ''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 2
2 × 11 = 44 and 3
2 × 5 =
45. The next such cluster of two square-primes comprises 2
2 × 29 =
116, and 3
2 × 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 44
2 + 1 = 1937 is 149 and thus more than 44 twice, 44 is a
Størmer number. 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, preceded by 7, 13, and 24, whose sum it equals.
44 is the number of
derangements of 5 items.
There are only 44 kinds of
Schwarz triangles, aside from the infinite
dihedral 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 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 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 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'' 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