17006
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 27864
- Proper Divisor Sum (Aliquot Sum)
- 10858
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 7720
- Möbius Function
- -1
- Radical
- 17006
- Omega Function (Ω)
- 3
- Little Omega Function (ω)
- 3
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
- 84
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Appears in sequences
- a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A008578 ({1} U primes).at n=36A023862
- a(n)-th and (a(n)+1)-st primes are the first pair of primes that differ by exactly 2n; a(n) = -1 if no such pair of primes exists.at n=38A038664
- a(n) = Bell(n+1)-Bell(n)-1, n>0.at n=8A052834
- a(n) = number of m such that A080737(m) <= 2n.at n=43A080740
- a(n) = A051707(A025487).at n=26A108460
- Number of indecomposable partitions of n.at n=35A122697
- a(n) = p(n)*p(n+2) - 3*p(n+1), where p(n) is the n-th prime.at n=30A152528
- Least number x such that there are n numbers of the form 6k-1 or 6k+1 between prime(x) and prime(x+1).at n=25A213903
- Numbers n such that n^1024 + (n+1)^1024 is prime.at n=26A274234
- a(n)=position of the first occurrence of a local maximum equal to 2n in A001223, n>1.at n=37A286729
- The n-th number m such that a nontrivial prime(n)-th root of unity modulo m exists.at n=43A305828
- a(n) = s(n,n) + s(n,n-1) + s(n,n-2), where s(n,k) are the unsigned Stirling numbers of the first kind (see A132393).at n=19A308305
- Number of smooth arithmetical structures on D_n.at n=34A335675
- a(n) is the least integer k such that 1/(Sum_{j=1..n} 1/phi(k*j)) is an integer.at n=38A341810
- a(n) is the least k such that the number of integers between (1/4)*prime(k) and (1/4)*prime(k+1) is n.at n=18A390785
- a(n) is the least k such that the number of integers between (1/5)*prime(k) and (1/5)*prime(k+1) is n.at n=15A390786
- a(n) is the least k such that there are exactly n integers between (1/6)*prime(k) and (1/6)*prime(k+1).at n=12A390787
- a(n) is the least n-bit number k such that k has the maximum number of distinct (nonempty) substrings in the binary representation of k.at n=14A391787