44 (number)

Forty-four is a repdigit and palindromic number in decimal. It is the tenth 10-happy number,{{Cite web|url=https://oeis.org/A007770|title=Sloane's A007770 : Happy numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}} and the fourth octahedral number.{{Cite web|url=https://oeis.org/A005900|title=Sloane's A005900 : Octahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}

It is a square-prime of the form p² × 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 p² × 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 of 40, within an aliquot sequence 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.{{Cite web|url=https://oeis.org/A005528|title=Sloane's A005528 : Størmer numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}} Given Euler's totient function, φ(44) = 20 and φ(69) = 44.

44 is a tribonacci number, preceded by 7, 13, and 24, whose sum it equals.{{Cite web|url=https://oeis.org/A000073|title=Sloane's A000073 : Tribonacci numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}

44 is the number of derangements of 5 items.{{Cite web|url=https://oeis.org/A000166|title=Sloane's A000166 : Subfactorial or rencontres numbers, or derangements|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}

There are only 44 kinds of Schwarz triangles, aside from the infinite dihedral family of triangles (p 2 2) with p = {2, 3, 4, ...}.{{Cite journal |last=Messer |first=Peter W. |url=https://link.springer.com/content/pdf/10.1007/s00454-001-0078-2.pdf |title=Closed-Form Expressions for Uniform Polyhedra and Their Duals |journal=Discrete & Computational Geometry |year=2002 |volume=27 |issue=3 |publisher=Springer |pages=353–355; 372–373 |doi=10.1007/s00454-001-0078-2 |doi-access=free |mr=1921559 |s2cid=206996937 |zbl=1003.52006 }}

There are 44 distinct stellations of the truncated cube and truncated octahedron, per Miller's rules.{{Cite web |url=https://www.software3d.com/Enumerate.php |last=Webb |first=Robert |title=Enumeration of Stellations |website=www.software3d.com |access-date=2022-11-25 |archive-url=https://archive.today/20221126015207/https://www.software3d.com/Enumerate.php |archive-date=2022-11-26 }}

44 four-dimensional crystallographic point groups of a total 227 contain dual enantiomorphs, or mirror images.{{Cite journal |last=Souvignier |first=Bernd |url=https://www.researchgate.net/publication/10787236 |title=Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6 |journal=Acta Crystallographica Section A |volume=59 |year=2003 |issue=3 |pages=217 |doi=10.1107/s0108767303004161 |pmid=12714771 |zbl=1370.20045 |s2cid=26198482 }}

There are forty-four classes of finite simple groups that arise from four general families of such groups:

• Two general groups stem from cyclic groups and alternating groups.
• Sixteen families of groups stem from simple groups of Lie type.
• Twenty-six groups are sporadic.

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.

Forty-four is:

• Mark Twain's The Mysterious Stranger features Satan'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

{{reflist}}

{{Integers|zero}}

Category:Integers