13920
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
- 48
- Divisor Sum
- 45360
- Proper Divisor Sum (Aliquot Sum)
- 31440
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3584
- Möbius Function
- 0
- Radical
- 870
- Omega Function (Ω)
- 8
- Little Omega Function (ω)
- 4
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
- yes
- Narcissistic Number
- no
- Collatz Steps
- 32
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- 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
- yes
- Odd
- no
Appears in sequences
- Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.at n=28A006863
- Number of points on surface of 4-dimensional cube.at n=12A008511
- Expansion of Product_{m>=1} (1-m*q^m)^24.at n=5A022684
- a(n) = n*(n - 1)*(n + 2)/2.at n=29A077414
- Largest number m such that a^n == 1 (mod m) whenever a is coprime to m.at n=55A079612
- Numbers k such that 2k-1 divides 2^k-1.at n=14A081856
- Largest integer m such that m divides (sigma_(2n+1)(2k-1)-sigma(2k-1)) for all k>=1.at n=27A081863
- a(n) = denominator of b(n): b(n) = the maximum possible value for a continued fraction whose terms are a permutation of the terms of the simple continued fraction for H(n) = sum{k=1 to n} 1/k, the n-th harmonic number.at n=14A129083
- Strongly refactorable numbers: numbers n such that if n is divisible by d, it is divisible by the number of divisors of d.at n=20A141586
- a(1) = 1, a(2) = 10, a(n+2) = 10*a(n+1) + (n + 1)*(n + 2)*a(n).at n=4A142987
- Largest number k such that the reduced totient function psi(k) = A002174(n).at n=23A143407
- Positive integers n such that n^2 = (x^4 - y^4)*(z^4 - t^4) where the pairs of integers (x,y) and (z,t) are not proportional.at n=14A147854
- Positive integers n such that n^2 = (x^4 - y^4)*(z^4 - t^4) where x>y and z>t are distinct pairs of integers with gcd(x,y)=gcd(z,t)=1.at n=7A147856
- Differences of two coprime 4th powers.at n=41A147858
- a(n) = n*(n^2+4).at n=24A155965
- Expansion of (eta(q^2)^7 / eta(q^4)^2)^4 + 16 * (eta(q)^2 * eta(q^2) * eta(q^4)^2)^4 in powers of q.at n=9A173763
- Numbers of the form p^5*q*r*s where p, q, r, and s are distinct primes.at n=12A179704
- a(n) counts the distinct cubical (on alphabet of 3 symbols) billiard words with length n, acting as prefix to just k = 2 such words of length n+1 (that is, a subset of "special").at n=16A180438
- E.g.f.: A(x) = Product_{n>=1} (1 + 2*x^n/n)^n.at n=6A182965
- Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}.at n=44A193893