44 (number)

44 (forty-four) is the natural number following 43 and preceding 45.

Forty-four is a repdigit and palindromic number in decimal. It is the tenth 10-happy number,^[1] and the fourth octahedral number.^[2]

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.^[3] 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.^[4]

44 is the number of derangements of 5 items.^[5]

There are only 44 kinds of Schwarz triangles, aside from the infinite dihedral family of triangles (p 2 2) with p = {2, 3, 4, ...}.^[6]

There are 44 distinct stellations of the truncated cube and truncated octahedron, per Miller's rules.^[7]

44 four-dimensional crystallographic point groups of a total 227 contain dual enantiomorphs, or mirror images.^[8]

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 Resident's Live at the Fillmore album, the number 44 is a main focus.