Natural number
225 (two hundred [and] twenty-five ) is the natural number following224 and preceding226 .
225 is the smallest number that is apolygonal number in five different ways.[ 1] square number (225 = 152 ) ,[ 2] octagonal number ,[ 3] squared triangular number (225 = (1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53 ) .[ 4]
As the square of adouble factorial ,225 = 5!!2 counts the number ofpermutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length.[ 5] Stirling numbers of the first kind , it counts the number of permutations of six items with exactly three cycles.[ 6]
225 is ahighly composite odd number , meaning that it has more divisors than any smaller odd numbers.[ 7] n for whichσ (φ (n )) =φ (σ (n ))σ is thesum of divisors function andφ isEuler's totient function .[ 8] refactorable number .[ 9]
225 is the smallestsquare 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]
^ Sloane, N. J. A. (ed.)."Sequence A063778 (a(n) = the least integer that is polygonal in exactly n ways)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000290 (The squares)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000567 (Octagonal numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000537 (Sum of first n cubes; or n-th triangular number squared)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A001818 (Squares of double factorials)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000399 (Unsigned Stirling numbers of first kind s(n,3))" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A053624 (Highly composite odd numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A033632 (Numbers n such that sigma(phi(n)) = phi(sigma(n)))" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ "Sloane's A033950 : Refactorable numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. 2016-04-18. Retrieved2016-04-18 .^ Sloane, N. J. A. (ed.)."Sequence A061845 (Numbers which have one of every digit in some base)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000005 (the number of divisors of n)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.
400 to 999
400s, 500s, and 600s 700s, 800s, and 900s
1000s and 10,000s
1000s 10,000s
100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
