46 (number)

Forty-six is

• thirteenth discrete semiprime ($2\; \backslash times\; 23$) 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,{{Cite web|url=https://oeis.org/A001190|title=Sloane's A001190 : Wedderburn-Etherington numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30|archive-date=2011-03-17|archive-url=https://web.archive.org/web/20110317001516/https://oeis.org/A001190|url-status=live}}
• the second non-trivial enneagonal number, after 24,{{Cite web|url=https://oeis.org/A001106|title=Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30|archive-date=2016-06-10|archive-url=https://web.archive.org/web/20160610053219/https://oeis.org/A001106|url-status=live}}
• a centered triangular number,{{Cite web|url=https://oeis.org/A005448|title=Sloane's A005448 : Centered triangular numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30|archive-date=2018-12-26|archive-url=https://web.archive.org/web/20181226080836/https://oeis.org/A005448|url-status=live}}
• the number of parallelogram polyominoes with 6 cells.{{cite OEIS|A006958|Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)}}
• the amount of prime numbers in between 1 and 200.

It is the sum of the totient function for the first twelve integers.{{Cite web|url=https://oeis.org/A002088|title=Sloane's A002088 : Sum of totient function|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30|archive-date=2017-12-06|archive-url=https://web.archive.org/web/20171206000024/http://oeis.org/A002088|url-status=live}} 46 is the largest even integer that cannot be expressed as a sum of two abundant numbers. It is also the sixteenth semiprime.{{OEIS|A001358}}

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.{{Cite web|url=https://oeis.org/A059756|title=Sloane's A059756 : Erdős-Woods numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30|archive-date=2017-12-21|archive-url=https://web.archive.org/web/20171221020206/http://oeis.org/A059756|url-status=live}}

The friendly giant $\backslash mathbb\; \{F\_1\}$, the largest of twenty-six sporadic groups, holds a total of forty-six maximal subgroups.{{efn|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,{{Cite OEIS |A039653 |a(n) as sigma(n)-1 |access-date=2024-07-26 }} which is the largest prime number to only divide the group order of $\backslash mathbb\; \{F\_1\}$. }}

• The number of mountains in the 46 peaks of the Adirondack mountain range. People who have climbed all of them are called "forty-sixers".{{Cite web|title=Hiking Challenges: The Adirondack 46ers|url=https://www.adirondack.net/hiking/challenges/46er/|access-date=2020-08-23|website=Adirondack.net|language=en-US|archive-date=2020-09-22|archive-url=https://web.archive.org/web/20200922052908/https://www.adirondack.net/hiking/challenges/46er/|url-status=live}}

File:Flag of Oklahoma (1911–1925).svg (1911–1925)]]

Forty-six is also:

• 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.
• The first Flag of Oklahoma, adopted by the state in 1911, had the number 46 written in blue inside the star, as Oklahoma was the forty-sixth state to join the Union (the United States).
• Joe Biden is the 46th President of the United States.

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{{Integers|zero}}

Category:Integers