313
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 7
- Digital Root
- 7
- Palindromic Number
- yes
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 314
- 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
- 312
- Möbius Function
- -1
- Radical
- 313
- 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
- 130
- 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
- 65
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- dreihundertdreizehn· ordinal: dreihundertdreizehnste
- English
- three hundred thirteen· ordinal: three hundred thirteenth
- Spanish
- trescientos trece· ordinal: 313º
- French
- trois cent treize· ordinal: trois cent treizième
- Italian
- trecentotredici· ordinal: 313º
- Latin
- trecenti tredecim· ordinal: 313.
- Portuguese
- trezentos e treze· ordinal: 313º
Appears in sequences
- Number of equivalence classes of nonzero regular 0-1 matrices of order n.at n=7A000519
- Numbers that are not the sum of 4 tetrahedral numbers.at n=24A000797
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=15A000921
- Wagstaff numbers: numbers k such that (2^k + 1)/3 is prime.at n=17A000978
- a(n) = ceiling(n^2/2).at n=25A000982
- Numbers k such that sum of squares of k consecutive integers >= 1 is a square.at n=36A001032
- 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=24A001033
- Union of all numbers {p, q} where p and q are both primes or powers of primes and q = p+2.at n=55A001092
- Twin primes.at n=38A001097
- Primes == +-1 (mod 8).at n=29A001132
- Indices of prime Lucas numbers.at n=20A001606
- 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=12A001844
- Full reptend primes: primes with primitive root 10.at n=23A001913
- Primes p such that the congruence 2^x == 3 (mod p) is solvable.at n=37A001915
- Nearest integer to n^2/8.at n=50A001971
- Palindromes in base 10.at n=40A002113
- Pythagorean primes: primes of the form 4*k + 1.at n=29A002144
- 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=30A002313
- Let p = A007645(n) be the n-th generalized cuban prime and write p^2 = x^2 + 3*y^2 with y > 0; a(n) = x.at n=37A002367
- Palindromic primes: prime numbers whose decimal expansion is a palindrome.at n=10A002385