4002
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 6
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 8640
- Proper Divisor Sum (Aliquot Sum)
- 4638
- 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
- 1232
- Möbius Function
- 1
- Radical
- 4002
- Omega Function (Ω)
- 4
- 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
- 51
- 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
- yes
- Odd
- no
Appears in sequences
- Expansion of chi(x)^10 / phi(x)^4 in powers of x where phi(), chi() are Ramanujan theta functions.at n=14A002512
- Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice.at n=20A005901
- 'Eban' numbers (the letter 'e' is banned!).at n=40A006933
- Some permutation of digits is a factorial number.at n=37A007926
- Some nontrivial permutation of digits is a factorial number.at n=31A007927
- Coordination sequence T4 for Zeolite Code DOH.at n=39A008081
- Coordination sequence T2 for Zeolite Code LEV.at n=47A008128
- Coordination sequence T1 for Zeolite Code STI.at n=43A008234
- Coordination sequence for diamond.at n=40A008253
- Coordination sequence for CaF2(2), Ca position.at n=40A009926
- a(0) = 1, a(n) = 40*n^2 + 2 for n>0.at n=10A010022
- a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0, a(1) = 9.at n=14A022314
- n written in fractional base 8/4.at n=34A024646
- 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=23A025113
- Triangle T by rows: second differences of Motzkin triangle (A026300), (i >= -1, -1<=j<=i).at n=74A026120
- a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.at n=8A026124
- Conjecturally, a power of 2 written in base 3 cannot have this many 0's.at n=32A036462
- Denominators of continued fraction convergents to sqrt(347).at n=9A041657
- Revert transform of (-1 + x + x^2)/((x - 1)*(x + 1)).at n=8A049124
- a(n) = T(2n-1,n) + T(2n,n+1) + ... + T(3n-3,2n-2) = sum over a period of n-th diagonal of array T given by A049828.at n=48A049833