1680
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 15
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 40
- Divisor Sum
- 5952
- Proper Divisor Sum (Aliquot Sum)
- 4272
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 384
- Möbius Function
- 0
- Radical
- 210
- 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
- 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
- 42
- 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^2*Product_{p|n} (1 + 1/p).at n=34A000082
- Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.at n=22A000099
- Number of ways of writing n as a sum of 5 squares.at n=29A000132
- Triangle of numbers related to triangle A049213; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497.at n=25A000369
- First occurrence of n consecutive numbers that take same number of steps to reach 1 in 3x+1 problem.at n=8A000546
- Octagonal numbers: n*(3*n-2). Also called star numbers.at n=24A000567
- Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.at n=14A000604
- Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, ...at n=47A001082
- Number of n-step polygons on f.c.c. lattice.at n=4A001337
- a(n) = n!/24.at n=4A001720
- Quadruple factorial numbers: a(n) = (2n)!/n!.at n=4A001813
- Highly abundant numbers: numbers k such that sigma(k) > sigma(m) for all m < k.at n=50A002093
- Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=16A002182
- G.f.: q * Product_{m>=1} (1-q^m)^8*(1-q^2m)^8.at n=10A002288
- a(n) = n! / 3.at n=4A002301
- Numbers of the form (p^2 - 1)/120 where p is 1 or prime.at n=41A002381
- Specific heat for diamond.at n=4A002922
- Smallest integer m such that the product of every 4 consecutive integers > m has a prime factor > prime(n).at n=10A003033
- Smallest number with 2n divisors.at n=19A003680
- Superabundant [or super-abundant] numbers: n such that sigma(n)/n > sigma(m)/m for all m < n, sigma(n) being A000203(n), the sum of the divisors of n.at n=16A004394