13205
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 16800
- Proper Divisor Sum (Aliquot Sum)
- 3595
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 9936
- Möbius Function
- -1
- Radical
- 13205
- 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
- 138
- 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) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (odd natural numbers), t = A000201 (lower Wythoff sequence).at n=35A025113
- Base-9 palindromes that start with 2.at n=21A043029
- Numbers whose base-7 representation contains exactly four 3's.at n=28A043408
- Pisot sequence L(9,10).at n=25A048592
- T(n,n-5), where T is the array in A055830.at n=18A055832
- Partial sums of first m composite numbers arising in A053781.at n=8A073262
- Number of configurations of the 6 X 2 variant of the so-called "Sam Loyd" sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.at n=19A090167
- Expansion of g.f.: 1/((1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7)*(1 + x + x^2 + x^3 + x^4 + x^5 - x^7)).at n=25A147605
- 5 times centered pentagonal numbers: 5*(5*n^2 + 5*n + 2)/2.at n=32A164015
- A255446(2^n-1).at n=7A255447
- Palindromic numbers in bases 3 and 9 written in base 10.at n=43A259386
- Number of 2-ascent sequences of length n with no consecutive repeated letters.at n=8A263852
- Number A(n,k) of k-ascent sequences of length n with no consecutive repeated letters; square array A(n,k), n>=0, k>=0, read by antidiagonals.at n=63A264909
- Starting at n, a(n) is the length of the smallest interval containing all points visited according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away.at n=7A324673
- Number of quadrilateral regions in a "frame" of size n X n (see Comments in A331776 for definition), divided by 8.at n=22A332596
- Numbers k whose ordered binary weights (A000120) of their divisors are the numbers 1 to A000005(k).at n=38A354724
- Number of partitions of n with rank 4 (the rank of a partition is the largest part minus the number of parts).at n=52A363213
- Numbers m such that 18*m + 1, 36*m + 1, 108*m + 1, and 162*m + 1 are all primes.at n=39A372188