8191
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 19
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 8192
- 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
- 8190
- Möbius Function
- -1
- Radical
- 8191
- 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
- 158
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- yes
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1028
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)at n=13A000225
- Mersenne primes (primes of the form 2^n - 1).at n=4A000668
- Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.at n=24A001265
- Mersenne numbers: 2^p - 1, where p is prime.at n=5A001348
- a(n) = least primitive factor of 2^(2n+1) - 1.at n=6A002184
- Primes of form k^2 + k + 1.at n=30A002383
- a(n) = largest noncomposite factor of 2^(2n+1) - 1.at n=6A002588
- Numerators of the Taylor coefficients of (e^x-1)^2.at n=12A002678
- Largest prime factor of n-th Mersenne number (A001348(n)).at n=5A003260
- Primes of form (p^x - 1)/(p^y - 1), p prime.at n=17A003424
- Divisors of 2^26 - 1.at n=3A003534
- Divisors of 2^39 - 1.at n=4A003545
- Class 1+ primes: primes of the form 2^i*3^j - 1 with i, j >= 0.at n=24A005105
- Largest prime factor of 2^n - 1.at n=24A005420
- Largest prime factor of 2^n - 1.at n=11A005420
- Mersenne numbers with at most 2 prime factors.at n=5A006515
- Numbers k such that k and k+1 are prime powers.at n=10A006549
- If n mod 4 = 0 then 2^(n-1)+1 elif n mod 4 = 2 then 2^(n-1)-1 else 2^(n-1).at n=13A007679
- Numbers n such that game of n X n Button Madness need have no solution; this lists only the primitive elements of the set.at n=12A007802
- Stirling numbers of second kind S2(14,n).at n=1A011563