44 (number)

Last updated
43 44 45
Cardinal forty-four
Ordinal 44th
(forty-fourth)
Factorization 22 × 11
Divisors 1, 2, 4, 11, 22, 44
Greek numeral ΜΔ´
Roman numeral XLIV
Binary 1011002
Ternary 11223
Senary 1126
Octal 548
Duodecimal 3812
Hexadecimal 2C16

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

Contents

In mathematics

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 finite simple groups.

In science

Astronomy

In technology

In other fields

Forty-four is:

Born from a foreign mother, his blood of ancient heroes,
And his name will be forty and four.

Historical years

AD 44 , 44 BC, 1944, etc.

See also

Related Research Articles

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

21 (twenty-one) is the natural number following 20 and preceding 22.

45 (forty-five) is the natural number following 44 and preceding 46.

22 (twenty-two) is the natural number following 21 and preceding 23.

26 (twenty-six) is the natural number following 25 and preceding 27.

28 (twenty-eight) is the natural number following 27 and preceding 29.

35 (thirty-five) is the natural number following 34 and preceding 36.

85 (eighty-five) is the natural number following 84 and preceding 86.

34 (thirty-four) is the natural number following 33 and preceding 35.

39 (thirty-nine) is the natural number following 38 and preceding 40.

46 (forty-six) is the natural number following 45 and preceding 47.

52 (fifty-two) is the natural number following 51 and preceding 53.

55 (fifty-five) is the natural number following 54 and preceding 56.

57 (fifty-seven) is the natural number following 56 and preceding 58.

58 (fifty-eight) is the natural number following 57 and preceding 59.

63 (sixty-three) is the natural number following 62 and preceding 64.

92 (ninety-two) is the natural number following 91 and preceding 93.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

138 is the natural number following 137 and preceding 139.

<span class="mw-page-title-main">146 (number)</span> Natural number

146 is the natural number following 145 and preceding 147.

References

  1. "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  3. "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  5. "Sloane's A000166 : Subfactorial or rencontres numbers, or derangements". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. Messer, Peter W. (2002). "Closed-Form Expressions for Uniform Polyhedra and Their Duals" (PDF). Discrete & Computational Geometry . 27 (3). Springer: 353–355, 372–373. doi: 10.1007/s00454-001-0078-2 . MR   1921559. S2CID   206996937. Zbl   1003.52006.
  7. Webb, Robert. "Enumeration of Stellations". www.software3d.com. Archived from the original on 2022-11-26. Retrieved 2022-11-25.
  8. Souvignier, Bernd (2003). "Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6". Acta Crystallographica Section A . 59 (3): 217. doi:10.1107/s0108767303004161. PMID   12714771. S2CID   26198482. Zbl   1370.20045.
  9. "Vicks Formula 44 oral: Uses, Side Effects, Interactions, Pictures, Warnings & Dosing - WebMD". www.webmd.com. Retrieved 2021-04-11.
  10. "The 15 Best Megadeth Songs: Critic's Picks". Billboard. Retrieved 2021-04-11.
  11. "O martírio do preso número 44". Jornal Observador (in Portuguese). Retrieved 2017-01-15.
  12. "José Sócrates é o recluso 44". Jornal Expresso (in European Portuguese). Retrieved 2021-04-11.