409
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 410
- 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
- 408
- Möbius Function
- -1
- Radical
- 409
- 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
- yes
- 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
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 80
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- vierhundertneun· ordinal: vierhundertneunste
- English
- four hundred nine· ordinal: four hundred ninth
- Spanish
- cuatrocientos nueve· ordinal: 409º
- French
- quatre cent neuf· ordinal: quatre cent neufième
- Italian
- quattrocentonove· ordinal: 409º
- Latin
- quadringenti novem· ordinal: 409.
- Portuguese
- quatrocentos e nove· ordinal: 409º
Appears in sequences
- Number of positive integers <= 2^n of form x^2 + 10 y^2.at n=11A000024
- Numbers beginning with letter 'f' in English.at n=33A000867
- Number of primes < prime(n)^2.at n=15A000879
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=18A000921
- 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=21A000928
- Numbers k such that sum of squares of k consecutive integers >= 1 is a square.at n=47A001032
- Numbers n such that the sum of the squares of n consecutive positive odd numbers x^2 + (x+2)^2 + ... + (x+2n-2)^2 = k^2 for some integer k. The least values of x and k for each n are in A056131 and A056132, respectively.at n=30A001033
- Primes == +-1 (mod 8).at n=36A001132
- Partial sums of A001462; also a(n) is the last occurrence of n in A001462.at n=48A001463
- Numbers n such that every digit contains a loop (version 2).at n=29A001744
- Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.at n=24A001914
- Primes p such that the congruence 2^x == 3 (mod p) is solvable.at n=46A001915
- Primes p such that the congruence 2^x = 5 (mod p) is solvable.at n=43A001916
- Pythagorean primes: primes of the form 4*k + 1.at n=38A002144
- Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 2.at n=63A002155
- Primes with record values of the least positive primitive root.at n=7A002230
- 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=39A002313
- Primes of the form 6m + 1.at n=37A002476
- Numbers k such that (k^2 + k + 1)/3 is prime.at n=49A002640
- Number of 4-line partitions of n (i.e., planar partitions of n with at most 4 lines).at n=10A002799