19
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 10
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 20
- Proper Divisor Sum (Aliquot Sum)
- 1
- 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
- 18
- Möbius Function
- -1
- Radical
- 19
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- 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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 20
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- yes
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 8
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Names
- German
- neunzehn· ordinal: neunzehnte
- English
- nineteen· ordinal: nineteenth
- Spanish
- diecinueve· ordinal: decimonoveno
- French
- dix-neuf· ordinal: dix-neufième
- Italian
- diciannove· ordinal: 19º
- Latin
- undeviginti· ordinal: 19.
- Portuguese
- dezenove· ordinal: 19º
Appears in sequences
- Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.at n=14A000008
- Smallest prime power >= n.at n=17A000015
- Smallest prime power >= n.at n=18A000015
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=18A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=18A000027
- Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.at n=10A000028
- Numbers that are not squares (or, the nonsquares).at n=14A000037
- Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.at n=6A000043
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=44A000052
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=13A000062
- Odious numbers: numbers with an odd number of 1's in their binary expansion.at n=9A000069
- a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).at n=5A000070
- Number of nonisomorphic minimal triangle graphs.at n=5A000080
- Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3.at n=4A000098
- Number of partitions into non-integral powers.at n=3A000158
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=11A000201
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=11A000202
- Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).at n=3A000223
- Number of squares mod n.at n=36A000224
- Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.at n=18A000265