421
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 7
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 422
- 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
- 420
- Möbius Function
- -1
- Radical
- 421
- 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
- 40
- 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
- 82
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- vierhunderteinundzwanzig· ordinal: vierhunderteinundzwanzigste
- English
- four hundred twenty-one· ordinal: four hundred twenty-first
- Spanish
- cuatrocientos veintiuno· ordinal: 421º
- French
- quatre cent vingt et un· ordinal: quatre cent vingt et unième
- Italian
- quattrocentoventuno· ordinal: 421º
- Latin
- quadringenti viginti unus· ordinal: 421.
- Portuguese
- quatrocentos e vinte e um· ordinal: 421º
Appears in sequences
- Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives A(A000099(n)).at n=9A000323
- Numbers k such that (1,k) is "good".at n=11A000696
- Numbers beginning with letter 'f' in English.at n=45A000867
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=19A000921
- 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=22A000928
- a(n) = ceiling(n^2/2).at n=29A000982
- a(n) = least m such that if a/b < c/d where a,b,c,d are integers in [0,n], then a/b < k/m < c/d for some integer k.at n=24A001000
- a(n) = ( Sum C(p,i); i=1,...,floor(2p/3) ) / p^2, where p = prime(n).at n=4A001007
- Twin primes.at n=42A001097
- Primes with primitive root 2.at n=33A001122
- Number of permutations of length n with longest increasing subsequence of length 5.at n=2A001456
- Smallest primitive prime factor of Fibonacci number F(n), or 1 if F(n) has no primitive prime factor.at n=20A001578
- Artiads: the primes p == 1 (mod 5) for which Fibonacci((p-1)/5) is divisible by p.at n=2A001583
- Nearest integer to 2*n*log(n).at n=53A001618
- Genus of modular group Gamma(n) = genus of modular curve Chi(n).at n=24A001767
- Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.at n=14A001844
- Primes p such that the congruence 2^x == 3 (mod p) is solvable.at n=48A001915
- Primes p such that the congruence 2^x = 5 (mod p) is solvable.at n=45A001916
- Nearest integer to n^2/8.at n=58A001971
- Central polygonal numbers: a(n) = n^2 - n + 1.at n=21A002061