8123
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 8124
- 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
- 8122
- Möbius Function
- -1
- Radical
- 8123
- 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
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1022
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A000201 (lower Wythoff sequence).at n=22A024464
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 89.at n=18A031587
- Number of 4-ary rooted trees with n nodes and height exactly 4.at n=20A036628
- Numbers whose base-4 representation contains exactly two 2's and four 3's.at n=25A045147
- Primes with first digit 8.at n=31A045714
- Discriminants of imaginary quadratic fields with class number 21 (negated).at n=22A046018
- Primes p such that number of primes produced according to rules stipulated in Honaker's A048853 is 4.at n=26A050666
- Numbers k such that 195*2^k-1 is prime.at n=49A050849
- First term of strong prime quintets: p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3).at n=23A054808
- Primes p such that x^31 = 2 has no solution mod p.at n=30A059225
- a(n) is the least odd number of the form p + k^2 with p prime and k > 0 which can be represented in exactly n different ways.at n=29A059400
- Gives an LCD representation of n.at n=39A071843
- a(1) = 1 and then the smallest primes such that all a(k)-a(j) are distinct composite numbers.at n=40A079850
- Class 5+ primes (for definition see A005105).at n=40A081633
- Primes p giving prime quadruples (30p+11, 30p+13, 30p+17, 30p+19).at n=8A087771
- Smallest number that can be written in binary representation as concatenation of other primes in exactly n ways.at n=19A090424
- Primes p such that q-p = 24, where q is the next prime after p.at n=12A098974
- Iccanobirt prime indices (6 of 15): Indices of prime numbers in A102116.at n=9A102136
- prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 8.at n=21A109562
- Column 1 of triangle A113983, also a(n) = [A113983^2](n-1,0) + 1.at n=10A113984