46 (number)

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

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, 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]
• 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.
• 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.

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 ${\displaystyle \mathbb {F_{1}} }$.