6585
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 24
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 10560
- Proper Divisor Sum (Aliquot Sum)
- 3975
- 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
- 3504
- Möbius Function
- -1
- Radical
- 6585
- 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
- 137
- 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
- Low temperature antiferromagnetic susceptibility for honeycomb lattice.at n=10A007214
- Expansion of (x/(1-x))*sqrt((1+x)/(1-3*x)).at n=9A025577
- Dirichlet convolution of 3^(n-1) with phi(n).at n=8A034754
- a(n) equals floor(Vc(n) - Vs(n)), where Vc(n) is the volume of the cube with side length n and Vs(n) is the volume of the sphere of diameter n.at n=23A057671
- Numbers k such that phi((prime(k)-1)/2) = sigma(k).at n=28A068474
- Trajectory of 442 under the Reverse and Add! operation carried out in base 2.at n=5A075268
- Numbers n such that zero is never reached by iterating the mapping k -> abs(reverse(lpd(k))-reverse(gpf(k))). lpd(k) is the largest proper divisor and gpf(k) is the largest prime factor of k.at n=15A076425
- Number of n X n binary arrays symmetric about both diagonal and antidiagonal with all ones connected only in a 1101-0111-0001 pattern in any orientation.at n=15A147235
- Positions of partition numbers in the EKG sequence.at n=30A159032
- Number of binary strings of length n with no substrings equal to 0000 0010 or 1010.at n=12A164422
- a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 10; a(0)=629, a(1)=6585, a(2)=26259, a(3)=221931, a(4)=1917027, a(5)=18285939, a(6)=125792217, a(7)=703932681, a(8)=7131271077, a(9)=26172260445, a(10)=103884128445.at n=1A177421
- a(n) = n^8+8n.at n=3A180358
- a(n)=(A210686(n)-1)/30.at n=34A181903
- Number of strings of numbers x(i=1..6) in 0..n with sum i^3*x(i) equal to 216*n.at n=15A184261
- E.g.f. A(x) satisfies A(x) = x*exp( A(x)*exp(A(x)) + A(x)^2*exp(2*A(x)) ).at n=4A189489
- Numbers 1 through 10000 sorted lexicographically in ternary representation.at n=42A190128
- q-expansion of modular form psi_0^6/t_{3B}^2.at n=12A198958
- a(n) = 3^n + 3*n.at n=8A221905
- a(n) = n*(15*n-11)/2.at n=30A226489
- Numbers m with C(2*m, m) - prime(m) prime, where C(2*m, m) = (2*m)!/(m!)^2.at n=26A236248