46 (number)

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

← 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, xlvi
Binary	1011102
Ternary	12013
Senary	1146
Octal	568
Duodecimal	3A12
Hexadecimal	2E16

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

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]
• the amount of prime numbers in between 1 and 200.

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. ^[a]

In sports

• 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. ^[9]

In other fields

Flag of Oklahoma (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.

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.). "SequenceA006958(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.). "SequenceA039653(a(n) as sigma(n)-1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-26.
9. "Hiking Challenges: The Adirondack 46ers". Adirondack.net. Archived from the original on 2020-09-22. Retrieved 2020-08-23.