Английская Википедия:225 (number)

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225 (two hundred [and] twenty-five) is the natural number following 224 and preceding 226.

In mathematics

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225 is the smallest number that is a polygonal number in five different ways.[1] It is a square number Шаблон:Nowrap,[2] an octagonal number,[3] and a squared triangular number Шаблон:Nowrap .[4]

As the square of a double factorial, Шаблон:Nowrap counts the number of permutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length.[5] And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles.[6]

225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers.[7] After 1 and 9, 225 is the third smallest number n for which Шаблон:Nowrap, where σ is the sum of divisors function and φ is Euler's totient function.[8] 225 is a refactorable number.[9]

225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) [10]

225 is the first odd number with exactly 9 divisors.[11]

References

Шаблон:Reflist

Шаблон:Integers

Шаблон:Num-stub