420
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 6
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 24
- Divisor Sum
- 1344
- Proper Divisor Sum (Aliquot Sum)
- 924
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 96
- Möbius Function
- 0
- Radical
- 210
- Omega Function (Ω)
- 5
- Little Omega Function (ω)
- 4
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
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 40
- Smith Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- 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
Classification
- Even
- yes
- Odd
- no
Names
- German
- vierhundertzwanzig· ordinal: vierhundertzwanzigste
- English
- four hundred twenty· ordinal: four hundred twentieth
- Spanish
- cuatrocientos veinte· ordinal: 420º
- French
- quatre cent vingt· ordinal: quatre cent vingtième
- Italian
- quattrocentoventi· ordinal: 420º
- Latin
- quadringenti viginti· ordinal: 420.
- Portuguese
- quatrocentos e vinte· ordinal: 420º
Appears in sequences
- Erroneous version of A032522.at n=13A000017
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=27A000114
- Number of discordant permutations.at n=2A000562
- Expansion of Product_{k >= 1} (1 - x^k)^6.at n=46A000729
- Number of compositions of n into 4 ordered relatively prime parts.at n=12A000742
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=20A000793
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=19A000793
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=22A000793
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=21A000793
- a(n) = Sum_{k = 1..n} floor(2^k / k).at n=10A000801
- Numbers beginning with letter 'f' in English.at n=44A000867
- a(n) = (4*n)! / ((2*n)!*n!^2).at n=2A000897
- a(n) = 5*binomial(n, 6).at n=9A000910
- a(n) = (2n+3)! /( n! * (n+1)! ).at n=2A000911
- Smallest even number that is an unordered sum of two odd primes in exactly n ways.at n=30A001172
- Maximal number of unattacked squares with n queens on n X n board (answers for n >= 17 only probable).at n=29A001366
- Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.at n=43A001484
- Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.at n=47A001484
- Triangle of coefficients of Bessel polynomials (exponents in decreasing order).at n=17A001497
- Triangle a(n,k) (n >= 0, 0 <= k <= n) of coefficients of Bessel polynomials y_n(x) (exponents in increasing order).at n=18A001498