10689
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 24
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 16320
- Proper Divisor Sum (Aliquot Sum)
- 5631
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6096
- Möbius Function
- -1
- Radical
- 10689
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 148
- Smith Number
- yes
- 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
- no
- Odd
- yes
Appears in sequences
- Number of 2 X 2 singular integer matrices with elements from {0,...,n}.at n=36A059306
- Index values for new maxima in A065925.at n=16A065926
- Interprimes (A024675) which are of the form s*prime, s=21.at n=26A075296
- Numerators of coefficients in function A(x) such that A(A(x)) = x+x^2.at n=11A097088
- a(n) = n^4 + 4*n^3 + 12*n^2 + 24*n + 24.at n=9A127878
- Number of n X n binary arrays symmetric about both diagonal and antidiagonal with all ones connected only in a 1010-1111 pattern in any orientation.at n=14A146425
- Number of n X n binary arrays symmetric under 180 degree rotation with all ones connected only in a 0100-0100-1111 pattern in any orientation.at n=9A146577
- Numbers that match polynomials over {0,1} that have a factor containing 3 as a coefficient; see Comments.at n=28A208181
- Numbers that match polynomials over {0,1} that have a factor containing -3 as a coefficient; see Comments.at n=8A208182
- G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^4 * x^n/n ), where Jacobsthal(n) = A001045(n).at n=5A211896
- Triangular array read by rows: T(n,k) is the number of partial permutations of {1,2,...,n} that have exactly k cycles, 0<=k<=n.at n=31A216294
- T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.at n=37A231523
- Number of 2 X n 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.at n=7A231524
- Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).at n=27A291350
- Number of ON cells after n generations of two-dimensional automaton based on knight moves (see Comments for definition; here a cell is turned ON if 1 or 2 neighbors are ON).at n=35A322055
- L.g.f.: -log( Sum_{n=-oo..+oo} (-p)^n * (p*x)^(n^2) ) = Sum_{n>=1} a(n) * x^n/n, where p = sqrt(2).at n=12A337948
- Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.at n=11A341405
- Numbers whose digits are distinct nonprimes and are not a permutation of a smaller such number.at n=59A359982
- Number of integer partitions of n with exactly as many ones as the next greatest multiplicity.at n=47A382303