8221
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 8222
- 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
- 8220
- Möbius Function
- -1
- Radical
- 8221
- 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
- 39
- 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
- yes
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1031
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Primes that divide at least one term of Sylvester's sequence s = A000058: s(n+1) = s(n)^2 - s(n) + 1, s(0) = 2.at n=22A007996
- Let q_k = p*(p+2) be product of k-th pair of twin primes; sequence gives values of p+2 such that (q_k)^2 > q_{k-i}*q_{k+i} for all 1 <= i <= k-1.at n=43A021007
- Primes that remain prime through 3 iterations of function f(x) = 2x + 9.at n=17A023276
- Primes that remain prime through 4 iterations of function f(x) = 2x + 9.at n=7A023306
- a(n+1) = [ A*a(n)+B ]/p^r, where p^r is the highest power of p diving [ A*a(n)+B ] and p=2, A=2.00013, B=3.0.at n=27A029580
- Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 16.at n=6A031604
- "BGK" (reversible, element, unlabeled) transform of 1,0,1,0,...at n=52A032059
- Primes p such that (p+1)/2 and (p+2)/3 are also primes.at n=22A036570
- Primes with indices that are primes with prime indices.at n=39A038580
- Primes with first digit 8.at n=40A045714
- Primes prime(k) for which A049076(k) = 3.at n=27A049079
- Recip transform of 2*(1 + x^2 + x^4)-1/(1-x).at n=12A049153
- Primes or negative values of primes in the sequence b(n) = 47*n^2 - 1701*n + 10181, n >= 0.at n=35A050267
- Least prime in A031928 (lesser of 10-twins) whose distance to the next 10-twin is 6*n.at n=20A052354
- Let prime(i) = i-th prime, let twin(n) = (P,Q) be n-th pair of twin primes; sequence gives prime(P).at n=36A057470
- Primes p such that p^6 reversed is also prime.at n=39A059699
- Primes with either no internal digits or all internal digits are 2.at n=48A069677
- Primes in A058633.at n=30A080822
- Class 5+ primes (for definition see A005105).at n=41A081633
- Twin-prime-indexed primes (TWIPS): members of a pair of twin primes whose prime index is also a member of a pair of twin primes.at n=26A087373