401
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 5
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 402
- 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
- 400
- Möbius Function
- -1
- Radical
- 401
- 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
- 19
- Smith Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 79
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- vierhunderteins· ordinal: vierhunderteinsste
- English
- four hundred one· ordinal: four hundred first
- Spanish
- cuatrocientos uno· ordinal: 401º
- French
- quatre cent un· ordinal: quatre cent unième
- Italian
- quattrocentouno· ordinal: 401º
- Latin
- quadringenti unus· ordinal: 401.
- Portuguese
- quatrocentos e um· ordinal: 401º
Appears in sequences
- Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) for n >= 4 with a(0) = a(1) = a(2) = 0 and a(3) = 1.at n=13A000078
- Number of bipartite partitions of n white objects and 3 black ones.at n=8A000412
- Number of rooted trees with n nodes, 2 of which are labeled.at n=4A000524
- Numbers beginning with letter 'f' in English.at n=25A000867
- 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=20A000928
- Primes with 3 as smallest primitive root.at n=17A001123
- Primes == +-1 (mod 8).at n=35A001132
- A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.at n=9A001259
- Nearest integer to 2*n*log(n).at n=51A001618
- A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7.at n=13A001635
- Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.at n=23A001914
- Primes p such that the congruence 2^x = 5 (mod p) is solvable.at n=42A001916
- Primes p == 1 (mod 4) where class number of Q(sqrt p) increases.at n=2A002142
- Pythagorean primes: primes of the form 4*k + 1.at n=37A002144
- Primes of the form 2^q*3^r*5^s + 1.at n=24A002200
- Primitive roots that go with the primes in A002230.at n=36A002229
- Primes congruent to 1 or 2 modulo 4; or, primes of form x^2 + y^2; or, -1 is a square mod p.at n=38A002313
- Primes of the form k^2 + 1.at n=7A002496
- a(n) = n^2 + 1.at n=20A002522
- Numbers k such that (k^2 + k + 1)/7 is prime.at n=38A002641