9
domain: N
Properties
Digital Properties
- Digit Count
- 1
- Digit Sum
- 9
- Digital Root
- 9
- Palindromic Number
- yes
- Repdigit
- yes
- Automorphic
- no
- Kaprekar Number
- yes
- Multiplicative Persistence
- 0
Divisibility
- Divisor Count
- 3
- Divisor Sum
- 13
- Proper Divisor Sum (Aliquot Sum)
- 4
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6
- Möbius Function
- 0
- Radical
- 3
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 1
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- yes
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- yes
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- yes
- Collatz Steps
- 19
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- Squarefree Number
- no
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- yes
- Achilles Number
- no
- Perfect Power
- yes
- Smooth Number
- yes
- Carmichael Number
- no
Names
- German
- neun· ordinal: neunte
- English
- nine· ordinal: ninth
- Spanish
- nueve· ordinal: noveno
- French
- neuf· ordinal: neuvième
- Italian
- nove· ordinal: nono
- Latin
- novem· ordinal: nonus
- Portuguese
- nove· ordinal: nono
Appears in sequences
- Number of classes of primitive positive definite binary quadratic forms of discriminant D = -4n; or equivalently the class number of the quadratic order of discriminant D = -4n.at n=58A000003
- Number of classes of primitive positive definite binary quadratic forms of discriminant D = -4n; or equivalently the class number of the quadratic order of discriminant D = -4n.at n=82A000003
- d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.at n=35A000005
- d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.at n=99A000005
- Integer part of square root of n-th prime.at n=22A000006
- Integer part of square root of n-th prime.at n=23A000006
- Integer part of square root of n-th prime.at n=24A000006
- Number of n-bead necklaces (turning over is allowed) where complements are equivalent.at n=7A000011
- Smallest prime power >= n.at n=8A000015
- Number of primitive permutation groups of degree n.at n=9A000019
- Number of primitive permutation groups of degree n.at n=12A000019
- Number of primitive permutation groups of degree n.at n=20A000019
- Number of primitive permutation groups of degree n.at n=44A000019
- Number of primitive permutation groups of degree n.at n=49A000019
- Number of primitive permutation groups of degree n.at n=55A000019
- Number of primitive permutation groups of degree n.at n=59A000019
- Number of positive integers <= 2^n of form x^2 + 12 y^2.at n=5A000021
- Number of centered hydrocarbons with n atoms.at n=8A000022
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=26A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=8A000027