46 (number)

"Forty-six" redirects here. For other uses, see 46 (disambiguation).

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

← 45 46 47 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-six
Ordinal	46th (forty-sixth)
Factorization	2 × 23
Divisors	1, 2, 23, 46
Greek numeral	ΜϚ´
Roman numeral	XLVI
Binary	1011102
Ternary	12013
Senary	1146
Octal	568
Duodecimal	3A12
Hexadecimal	2E16

In mathematics

Forty-six is

• thirteenth discrete semiprime (${\displaystyle 2\times 23}$) and the eighth of the form (2.q), where q is a higher prime,
• with an aliquot sum of 26; a semiprime, in an aliquot sequence of six composite numbers (46, 26,16, 15, 9, 4, 3, 1, 0) in the prime 3-aliquot tree,
• a Wedderburn-Etherington number,^[1]
• the second non-trivial enneagonal number, after 24,^[2]
• a centered triangular number,^[3]
• the number of parallelogram polyominoes with 6 cells.^[4]

It is the sum of the totient function for the first twelve integers.^[5] 46 is the largest even integer that cannot be expressed as a sum of two abundant numbers. It is also the sixteenth semiprime.^[6]

Since it is possible to find sequences of 46+1 consecutive integers such that each inner member shares a factor with either the first or the last member, 46 is an Erdős–Woods number.^[7]

The friendly giant ${\displaystyle \mathbb {F_{1}} }$, the largest of twenty-six sporadic groups, holds a total of forty-six maximal subgroups.^{[lower-alpha 1]}

In science

• The atomic number of palladium.
• The number of human chromosomes.^[9]
• The approximate molar mass of ethanol (46.07 g mol⁻¹)

Astronomy

• Messier object M46, a magnitude 6.5 open cluster in the constellation Puppis.
• The New General Catalogue object NGC 46, a star in the constellation Pisces.

In music

• Japanese idol group franchise Sakamichi Series, which consists of Nogizaka46, Keyakizaka46, Hinatazaka46, and Yoshimotozaka46

In sports

• Valentino Rossi used 46 as his number in the MotoGP world motorcycle championship.
• The number of mountains in the 46 peaks of the Adirondack mountain range. People who have climbed all of them are called "forty-sixers"; there is also an unofficial 47th peak.^[10]
• The name of a defensive scheme used in American football; see 46 defense.
• Local golfing “talent” Dave Kershaw shot 46 over at Les Ormes on the 21st July after predicting an “Under 20 over” round. Fans and onlookers could only describe his golf as “Horror”.

In religion

• The total of books in the Old Testament, Catholic version, if the Book of Lamentations is counted as a book separate from the Book of Jeremiah
• The number of years taken to build the Temple of Jerusalem (Jn 2:20) Gospel of John
• The number of stars on Our Lady of Guadalupe's mantle

In other fields

Flag of Oklahoma (1911–1925)

Forty-six is also:

• The code for international direct dial phone calls to Sweden.
• The number of samurai, out of 47, who carried out the attack in the historical Ako vendetta; sometimes referred to as the 46 Ronin to discount the one samurai forced to turn back.
• In the title of the movie Code 46, starring Tim Robbins and Samantha Morton.
• Several routes numbered 46 exist throughout the world.
• Because 46 in Japanese can be pronounced as "yon roku", and "yoroshiku" (よろしく) means "my best regards" in Japanese, people sometimes use 46 for greeting.
• 46 is the number of the City Chevrolet and Superflo cars driven by Cole Trickle in the movie Days of Thunder.
• The number of the French department Lot.
• 46 is the number that unlocks the Destiny spaceship on the Sci-Fi TV show Stargate Universe. Dr. Rush discovers that the number 46 relates to the number of human chromosomes and begins sequencing different genetic codes to finally gain control of the ship's operating system. The episode was called "Humans".
• The number depicted in the first flag of Oklahoma (replaced in 1925), signifying the fact that Oklahoma was the 46th state to join the United States.
• Joe Biden was inaugurated as the 46th President of the United States on January 20, 2021.

See also

• List of highways numbered 46

Notes

1. Where the aliquot part of 46 is equal to the total number of sporadic groups that classify as finite simple groups (26), the sum of the strong divisors of 46 (i.e. 2, 23, and 46), is 71,^[8] which is the largest prime number to only divide the group order of ${\displaystyle \mathbb {F_{1}} }$.

References

1. "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2011-03-17. Retrieved 2016-05-30.
2. "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2016-06-10. Retrieved 2016-05-30.
3. "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2018-12-26. Retrieved 2016-05-30.
4. Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. "Sloane's A002088 : Sum of totient function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2017-12-06. Retrieved 2016-05-30.
6. (sequence A001358 in the OEIS)
7. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2017-12-21. Retrieved 2016-05-30.
8. Sloane, N. J. A. (ed.). "Sequence A039653 (a(n) as sigma(n)-1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-26.
9. Barbara J. Trask, "Human genetics and disease: Human cytogenetics: 46 chromosomes, 46 years and counting" Nature Reviews Genetics 3 (2002): 769. "Human cytogenetics was born in 1956 with the fundamental, but empowering, discovery that normal human cells contain 46 chromosomes."
10. "Hiking Challenges: The Adirondack 46ers". Adirondack.net. Archived from the original on 2020-09-22. Retrieved 2020-08-23.