9180
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 48
- Divisor Sum
- 30240
- Proper Divisor Sum (Aliquot Sum)
- 21060
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 2304
- Möbius Function
- 0
- Radical
- 510
- Omega Function (Ω)
- 7
- 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
- yes
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- yes
- 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
- 60
- 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
- Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^10 in powers of x.at n=26A001488
- Theta series of {E_6}* lattice.at n=26A005129
- Theta series of A_5 lattice.at n=40A008445
- Expansion of Product_{k>=1} (1 - x^k)^18.at n=8A010824
- a(n) = 2*n*(4*n - 1).at n=34A014635
- a(n) = dot_product(n,n-1,...2,1)*(5,6,...,n,1,2,3,4).at n=29A026060
- Product of the lengths of the cycle types of the permutation created by duality and reversal on the partitions of n.at n=14A036046
- a(n) = Sum_{i=0..2n} (-1)^i * T(i,2n-i), array T as in A049723.at n=38A049725
- Tritriangular numbers: a(n) = binomial(binomial(n,2),2) = n*(n+1)*(n-1)*(n-2)/8.at n=17A050534
- T(n,n-5), where T is the array in A055830.at n=16A055832
- a(n) = (n^3 + 5*n + 18)/6.at n=40A060163
- Consider 2n tennis players; a(n) is the number of matches needed to let every possible pair play each other.at n=7A062346
- When expressed in base 2 and then interpreted in base 9, is a multiple of the original number.at n=54A062850
- Numbers k such that sigma(k) = 2*usigma(k).at n=26A063880
- Number of length 3 walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part.at n=20A064043
- Prime(n^2) +/- n are primes.at n=34A064495
- a(n) = sum of modular offsets: mod[n+c,b]-(mod[n,b]+c) for c<=b<=n.at n=43A066809
- Numbers k such that sigma(k) divides sigma(sigma(k)).at n=17A066961
- Smallest triangular number which is a multiple (>1) of the n-th triangular number.at n=16A068084
- Triangular numbers which are products of triangular numbers larger than 1.at n=18A068143