13821
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
- 3
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 19584
- Proper Divisor Sum (Aliquot Sum)
- 5763
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 8640
- Möbius Function
- -1
- Radical
- 13821
- 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
- 58
- 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) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A000032 (Lucas numbers).at n=15A023861
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (Lucas numbers).at n=14A024858
- Zeckendorf expansion of n: repeatedly subtract the largest Fibonacci number you can until nothing remains. Little-endian concatenation of decimals.at n=33A035515
- Numbers whose base-4 representation contains exactly three 1's and four 3's.at n=18A045128
- Numbers n of the form k + reverse(k) for exactly three k.at n=34A071914
- Sum of terms in n-th row of A077316.at n=16A077318
- Smallest number that can be written in exactly n ways as a sum of distinct repdigits of its decimal digits.at n=33A131367
- Number of planar n X n X n binary triangular grids symmetric both under 120 degree rotation and reflection with no more than 12 ones in any 5 X 5 X 5 subtriangle.at n=11A153999
- Triangle A054521 * A157019, where A054521 = an infinite lower triangular matrix and A157019 = a vector [1, 2, 2, 4, 2, 8, 2, 10, 8, ...].at n=52A157031
- Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>3z.at n=19A212510
- Number of (n+3) X 10 0..2 matrices with each 4 X 4 subblock idempotent.at n=7A224727
- Number of partitions p of n such that (number of numbers in p of form 3k+1) < (number of numbers in p of form 3k+2).at n=42A241737
- Partial sums of A255744.at n=22A255765
- Poincaré series for hyperbolic reflection group with Coxeter diagram o---o-(5)-o---o.at n=23A265044
- Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 529", based on the 5-celled von Neumann neighborhood.at n=24A272748
- Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 806", based on the 5-celled von Neumann neighborhood.at n=7A273607
- Solution of the complementary equation a(n) = a(n-1) + a(n-2) + n*b(n-2), where a(0) = 1, a(1) = 3, b(0) = 2, and (a(n)) and (b(n)) are increasing complementary sequences.at n=14A296286
- a(n) = n*(n + 1)*(16*n - 1)/6.at n=17A304659