21
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 3
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 32
- Proper Divisor Sum (Aliquot Sum)
- 11
- 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
- 12
- Möbius Function
- 1
- Radical
- 21
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- yes
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- yes
- Triangular Number
- yes
- 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
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 7
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Names
- German
- einundzwanzig· ordinal: einundzwanzigste
- English
- twenty-one· ordinal: twenty-first
- Spanish
- veintiuno· ordinal: 21º
- French
- vingt et un· ordinal: vingt et unième
- Italian
- ventuno· ordinal: 21º
- Latin
- viginti unus· ordinal: 21.
- Portuguese
- vinte e um· ordinal: 21º
Appears in sequences
- Coefficients of the 3rd-order mock theta function f(q).at n=17A000025
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=20A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=20A000027
- Numbers that are not squares (or, the nonsquares).at n=16A000037
- Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1) + a(n-2) - a(n-13).at n=8A000044
- Number of primitive n-bead necklaces (turning over is allowed) where complements are equivalent.at n=9A000046
- -1 + number of partitions of n.at n=8A000065
- Odious numbers: numbers with an odd number of 1's in their binary expansion.at n=10A000069
- 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); sequence gives values of n where |P(n)| sets a new record.at n=5A000092
- Number of trees of diameter 4.at n=9A000094
- Number of asymmetrical dissections of n-gon.at n=2A000131
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=6A000134
- Number of partitions into non-integral powers.at n=3A000160
- Number of partitions of n into 6 squares.at n=86A000177
- Largest order of automorphism group of a tournament with n nodes.at n=6A000198
- Largest order of automorphism group of a tournament with n nodes.at n=7A000198
- Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).at n=8A000199
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=12A000201
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=12A000202
- a(n) = floor(n^2/3).at n=8A000212