# 46 (number)

 ← 45 46 47 →
Cardinal forty-six
Ordinal 46th
(forty-sixth)
Factorization 2 × 23
Divisors 1, 2, 23, 46
Roman numeral XLVI
Binary 1011102
Ternary 12013
Quaternary 2324
Quinary 1415
Senary 1146
Octal 568
Duodecimal 3A12
Vigesimal 2620
Base 36 1A36

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

## In mathematics

Forty-six is a Wedderburn-Etherington number, an enneagonal number and a centered triangular number. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that can't be expressed as a sum of two abundant numbers.

46 is the 16th semiprime. 46 is the third semiprime with a semiprime aliquot sum. The aliquot sequence of 46 is (46,26,16,15,9,4,3,1,0).

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

## In science

### Astronomy

• The Saros number of the solar eclipse series which began on April 1, 1371 BC[2] and ended on May 8, 91 BC. The duration of Saros series 46 was 1280.1 years, and it contained 72 solar eclipses.
• The Saros number of the lunar eclipse series which began on July 19, 1358 BC[3] and ended on October 8, 12. The duration of Saros series 46 was 1370.5 years, and it contained 77 lunar eclipses.

## In sports

• Valentino Rossi, one of the most successful motorcycle riders of all time, uses 46 as his number in the MotoGP motorcycle world championship, and has been using this number in homage to his father since he started racing as a youngster.
• 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.
• The name of a defensive scheme used in American football; see 46 defense.

## 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 corresponding to the word "ADAM" where A=1, D=4, M=40[4] (on the analogy of the numeric values of letters in ancient alphabets, such as Hebrew[5] and Greek[6]).
Flag of Oklahoma (1911–1925)

## In other fields

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 Ronins 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 popular Sci-Fi TV show Stargate Universe. Dr. Rush discovers that the number 46 relates to the amount 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.

## References

1. ^ 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."
2. ^ NASA Solar Eclipse Web Site: -1399 to -1300 ( 1400 BCE to 1301 BCE )
3. ^ NASA Lunar Eclipse Web Site: -1399 to -1300 ( 1400 BCE to 1301 BCE )
4. ^ Baker, Peter and Michael Lapidge (1995) Byrhtferth's Enchiridion. Oxford: OUP for The Early English Text Society, p.201
5. ^ http://www.qsm.co.il/Hebrew/GimatriaH.htm
6. ^ http://147.52.104.14/PROMWEB/ARXAIA/arxaioi_numbers.htm