225 (number)

Last updated

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

In mathematics

← 224 225 226 →
'"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"' '"`UNIQ−−nowiki−00000000−QINU`"'
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 smallest odd number with exactly nine divisors. [11]

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.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.