225 (number)

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

In mathematics

← 224 225 226 →
Cardinal two hundred twenty-five
Ordinal 225th
(two hundred twenty-fifth)
Factorization 32 × 52
Prime no
Greek numeral ΣΚΕ´
Roman numeral CCXXV, ccxxv
Binary 111000012
Ternary 221003
Senary 10136
Octal 3418
Duodecimal 16912
Hexadecimal E116

225 is the smallest number that is a polygonal number in five different ways. [1] It is a square number (225 = 152), [2] an octagonal number, [3] and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53) . [4]

As the square of a double factorial, 225 = 5!!2 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 σ(φ(n)) = φ(σ(n)), 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]

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96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when turned upside down.

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<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

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232 is the natural number following 231 and preceding 233.

252 is the natural number following 251 and preceding 253.

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA063778(a(n) = the least integer that is polygonal in exactly n ways)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA000290(The squares)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA000567(Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA000537(Sum of first n cubes; or n-th triangular number squared)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA001818(Squares of double factorials)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA000399(Unsigned Stirling numbers of first kind s(n,3))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA053624(Highly composite odd numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA033632(Numbers n such that sigma(phi(n)) = phi(sigma(n)))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. ↑ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
  10. ↑ Sloane, N. J. A. (ed.). "SequenceA061845(Numbers which have one of every digit in some base)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  11. ↑ Sloane, N. J. A. (ed.). "SequenceA000005(the number of divisors of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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