7072
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 24
- Divisor Sum
- 15876
- Proper Divisor Sum (Aliquot Sum)
- 8804
- 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
- 3072
- Möbius Function
- 0
- Radical
- 442
- Omega Function (Ω)
- 7
- 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
- yes
- Narcissistic Number
- no
- Collatz Steps
- 119
- 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
- a(n) = (n+1)*(n+3)*(n+8)/6.at n=32A000297
- The convergent sequence C_n for the ternary continued fraction (3,1;2,2) of period 2.at n=12A000964
- Number of n-node trees of height at most 5.at n=13A001385
- Fourth convolution of Catalan numbers: a(n) = 4*binomial(2*n+3,n)/(n+4).at n=7A002057
- Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,2).at n=6A005550
- a(n) = Sum_{k=1..n-1} lcm(k,n-k).at n=39A006580
- Shifts left when inverse Moebius transform applied twice.at n=40A007557
- Catalan's triangle T(n,k) (read by rows): each term is the sum of the entries above and to the left, i.e., T(n,k) = Sum_{j=0..k} T(n-1,j).at n=62A009766
- Catalan's triangle with right border removed (n > 0, 0 <= k < n).at n=52A030237
- Shifts left under COMPOSE transform.at n=4A030276
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 41.at n=32A031539
- Numbers whose set of base-12 digits is {1,4}.at n=23A032824
- a(n) is root of square starting with digit 5: first term of runs.at n=5A035072
- Triangle formed from odd-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x). Sometimes called Catalan's triangle.at n=37A039598
- Numbers n such that lcm(sigma(n),phi(n)) is a perfect square.at n=42A043293
- Row sums of triangle A049327.at n=4A049351
- T(n,k) = M(2n-1,n-1,k-1), 0 <= k <= n, n >= 0, where M(p,q,r) is the number of upright paths from (0,0) to (p,p-q) that meet the line y = x+r and do not rise above it.at n=47A050144
- T(n,k)=M(2n,n-1,k-1), 0<=k<=n, n >= 0, array M as in A050144.at n=46A050145
- T(n,k)=M(2n+2,n-1,k-1), 0<=k<=n, n >= 0, array M as in A050144.at n=36A050154
- T(n,k)=M(2n+3,n+3,k+3), 0<=k<=n, n >= 0, array M as in A050144.at n=28A050156