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225 (number)

FieldValue
number225
primeno
divisor1, 3, 5, 9, 15, 25, 45, 75, 225

In mathematics

225 is the smallest number that is a polygonal number in five different ways. It is a square number , an octagonal number, and a squared triangular number .

As the square of a double factorial, 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. And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles.

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

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

225 is the smallest odd number with exactly nine divisors.

References

References

  1. {{Cite OEIS. A063778
  2. {{Cite OEIS. A000290
  3. {{Cite OEIS. A000567
  4. {{Cite OEIS. A000537
  5. {{Cite OEIS. A001818
  6. {{Cite OEIS. A000399
  7. {{Cite OEIS. A053624
  8. {{Cite OEIS
  9. (2016-04-18). "Sloane's A033950 : Refactorable numbers". OEIS Foundation.
  10. {{Cite OEIS. A061845
  11. {{Cite OEIS. A000005
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