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44 (number)

Natural number From Wikipedia, the free encyclopedia

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

Quick facts ← 43 44 45 →, Cardinal ...
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In mathematics

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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:

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.

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In other fields

Forty-four is:

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