10563
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 15
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 16128
- Proper Divisor Sum (Aliquot Sum)
- 5565
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6024
- Möbius Function
- -1
- Radical
- 10563
- 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
- 55
- 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
- no
- Odd
- yes
Appears in sequences
- a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,2.at n=13A022862
- Numbers n such that the Reverse and Add! trajectory of n (presumably) does not reach a palindrome and does not join the trajectory of any term m < n.at n=5A063048
- 'Reverse and Add!' trajectory of 10563.at n=0A063063
- Number of length 3 walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part.at n=21A064043
- Interprimes (A024675) which are of the form s*prime, s=21.at n=25A075296
- Least k such that 10^(2n-1)+k is a brilliant number.at n=36A084476
- Numbers k such that the Reverse and Add! trajectory of k (presumably) does not reach a palindrome (with the exception of k itself) and does not join the trajectory of any term m < k.at n=6A088753
- a(n) = smallest non-palindromic k such that the Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A070788(n).at n=9A089494
- a(n) = 343*n - 70.at n=30A157374
- a(n) = n*(2*n^2 + 5*n + 19)/2.at n=21A163675
- Integers of the form (k+1)*(2k+1)/12.at n=41A164578
- The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]].at n=49A171145
- The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]].at n=50A171145
- An Ulam-type sequence: a(n) = n if n<=10; for n>10, a(n) = least number > a(n-1) which is a unique sum of 10 distinct earlier terms.at n=48A183533
- Numbers that match polynomials over {0,1} that have a factor containing 3 as a coefficient; see Comments.at n=26A208181
- Numbers that match polynomials over {0,1} that have a factor containing -3 as a coefficient; see Comments.at n=7A208182
- Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..5 array extended with zeros and convolved with -1,2,-1.at n=16A222040
- The first of 50 consecutive positive integers the sum of the squares of which is a square.at n=19A269451
- Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p).at n=50A282037
- Numbers k such that the Reverse and Add! trajectory of k (presumably) does not reach a palindrome and does not join the trajectory or one of the reverse numbers of the trajectory of any term m < k.at n=5A306232