821
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 822
- 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
- 820
- Möbius Function
- -1
- Radical
- 821
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 28
- Smith Number
- no
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
- 142
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- achthunderteinundzwanzig· ordinal: achthunderteinundzwanzigste
- English
- eight hundred twenty-one· ordinal: eight hundred twenty-first
- Spanish
- ochocientos veintiuno· ordinal: 821º
- French
- huit cent vingt et un· ordinal: huit cent vingt et unième
- Italian
- ottocentoventuno· ordinal: 821º
- Latin
- octingenti viginti unus· ordinal: 821.
- Portuguese
- oitocentos e vinte e um· ordinal: 821º
Appears in sequences
- Number of nonisomorphic minimal triangle graphs.at n=9A000080
- Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.at n=40A000124
- Numbers beginning with letter 'e' in English.at n=34A000873
- Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.at n=55A000928
- Lesser of twin primes.at n=31A001359
- Numbers k such that phi(k+2) = phi(k) + 2.at n=50A001838
- Full reptend primes: primes with primitive root 10.at n=49A001913
- 7th powers written backwards.at n=2A002140
- 7th powers written backwards.at n=20A002140
- Primes p with a Fibonacci primitive root g, i.e., such that g^2 = g + 1 (mod p).at n=42A003147
- Even numbers written backwards.at n=64A004093
- Powers of 2 written backwards.at n=7A004094
- Divisible only by primes congruent to 1 mod 5.at n=40A004615
- Class 3+ primes (for definition see A005105).at n=48A005107
- Class 3- primes (for definition see A005109).at n=41A005111
- Representation degeneracies for boson strings.at n=20A005293
- Numbers of Twopins positions.at n=16A005688
- a(n) = Sum_{k=1..n-1} (k OR n-k).at n=28A006583
- Long period primes: the decimal expansion of 1/p has period p-1.at n=50A006883
- Primes for which -10 is a primitive root.at n=54A007348