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Concept
45 (number)
Summary
45 (forty-five) is the natural number following 44 and preceding 46.
Forty-five is the smallest odd number that has more divisors than , and that has a larger sum of divisors than . It is the sixth positive integer with a square-prime prime factorization of the form , with and prime, and first of the form .
45 has an aliquot sum of 33 that is part of an aliquot sequence composed of five composite numbers (45, 33, 15, 9, 4, 3, 1, and 0), all of-which are rooted in the 3-aliquot tree. This is the longest aliquot sequence for an odd number up to 45.
Forty-five is the sum of all single-digit decimal digits: . It is, equivalently, the ninth triangle number.
Forty-five is also the fourth hexagonal number and the second hexadecagonal number, or 16-gonal number. It is also the second smallest triangle number (after 1 and 10) that can be written as the sum of two squares.
Since the greatest prime factor of is 1,013, which is much more than 45 twice, 45 is a Størmer number. In decimal, 45 is a Kaprekar number and a Harshad number.
Forty-five is a little Schroeder number; the next such number is 197, which is the 45th prime number.
Forty-five is conjectured from Ramsey number .
In the classification of finite simple groups, the Tits group is sometimes defined as a nonstrict group of Lie type or sporadic group, which yields a total of 45 classes of finite simple groups: two stem from cyclic and alternating groups, sixteen are families of groups of Lie type, and another twenty-six are strictly sporadic. Inside the largest sporadic group, the Friendly Giant , there exist at least 45 conjugacy classes of maximal subgroups, which includes the double cover of the second largest sporadic group .
The atomic number of rhodium
Messier object M45, a magnitude 1.4 open cluster in the constellation Taurus, also known as the Pleiades
The New General Catalogue object NGC 45, a magnitude 10.
Official source
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