613
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 10
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 614
- 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
- 612
- Möbius Function
- -1
- Radical
- 613
- 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
- 38
- 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
- 112
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- sechshundertdreizehn· ordinal: sechshundertdreizehnste
- English
- six hundred thirteen· ordinal: six hundred thirteenth
- Spanish
- seiscientos trece· ordinal: 613º
- French
- six cent treize· ordinal: six cent treizième
- Italian
- seicentotredici· ordinal: 613º
- Latin
- sescenti tredecim· ordinal: 613.
- Portuguese
- seiscentos e treze· ordinal: 613º
Appears in sequences
- Number of points of norm <= n^2 in square lattice.at n=14A000328
- Numbers beginning with letter 's' in English.at n=37A000870
- Primes p of the form 3k+1 such that -sqrt(p) < sum_{x=1..p} cos(2*Pi*x^3/p) < sqrt(p).at n=15A000922
- 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=36A000928
- Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.at n=27A000960
- a(n) = ceiling(n^2/2).at n=35A000982
- Primes with primitive root 2.at n=45A001122
- Associated Mersenne numbers.at n=17A001351
- Indices of prime Lucas numbers.at n=23A001606
- A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7.at n=14A001635
- 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=17A001844
- Pythagorean primes: primes of the form 4*k + 1.at n=52A002144
- 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=53A002313
- Primes of the form 6m + 1.at n=52A002476
- Numbers k such that (k^2 + k + 1)/21 is prime.at n=31A002644
- Discriminants of real quadratic fields with narrow class number 1.at n=49A003655
- Divisible only by primes congruent to 4 mod 7.at n=20A004622
- Divisible only by primes congruent to 5 mod 8.at n=41A004627
- Class 3+ primes (for definition see A005105).at n=37A005107
- Class 2- primes (for definition see A005109).at n=49A005110