7824
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 21
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 4
Divisibility
- Divisor Count
- 20
- Divisor Sum
- 20336
- Proper Divisor Sum (Aliquot Sum)
- 12512
- 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
- 2592
- Möbius Function
- 0
- Radical
- 978
- Omega Function (Ω)
- 6
- 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
- 52
- Smith Number
- yes
- 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
- Related to self-avoiding walks on square lattice.at n=7A006814
- a(n) = floor( n*(n-1)*(n-2)/29 ).at n=62A011911
- a(n) = prime(n)^2 - prime(n+1).at n=23A062235
- Number of hexagonal regions in regular n-gon with all diagonals drawn.at n=42A067153
- Total sum of prime parts in all partitions of n.at n=20A073118
- Numbers k such that the number of distinct primes dividing k = number of anti-divisors of k.at n=43A073713
- Erroneous version of A087316.at n=4A081744
- Binomial transform of A083580.at n=7A083586
- a(n) = Sum_{k=1..n} prime(k)^prime(n-k+1).at n=4A087316
- Triangle read by rows: T(n,k) is number of Dyck paths of semilength n and having k UDUD's (here U=(1,1), D=(1,-1)).at n=59A094507
- Expansion of (chi(-q^3)/ chi^3(-q) -1)/3 in powers of q where chi() is a Ramanujan theta function.at n=22A128129
- Triangle T, read by rows, where row n+1 of T = row n of matrix power T^(2n) with appended '1' for n>=0 with T(0,0)=1.at n=50A132610
- Expansion of q * psi(-q^9) / psi(-q) in powers of q where psi() is a Ramanujan theta function.at n=45A132975
- Expansion of q^(-1/3) * (eta(q^6)^4 / (eta(q) * eta(q^3) * eta(q^4) * eta(q^12)))^2 in powers of q.at n=15A132977
- Expansion of c(q^3) / (c(q^3) + c(q^6)) where c() is a cubic AGM function.at n=46A145977
- 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).at n=24A152760
- G.f. A(x) satisfies: A(x) = G(x*A(x)) where A(x/G(x)) = G(x) = g.f. of A004304, where A004304(n) is the number of planar tree-rooted maps with n edges.at n=6A168450
- Total number of parts that are neither the smallest part nor the largest part in all partitions of n.at n=26A182977
- G.f.: Sum_{n>=1} G_n(x)^n where G_n(x) = x + x*G_n(x)^n.at n=20A194560
- Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 3,2,2,4,2,2,0 for x=0,1,2,3,4,5,6.at n=5A197874