5040
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 9
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 60
- Divisor Sum
- 19344
- Proper Divisor Sum (Aliquot Sum)
- 14304
- 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
- 1152
- Möbius Function
- 0
- Radical
- 210
- Omega Function (Ω)
- 8
- Little Omega Function (ω)
- 4
Special
- Factorial
- yes
- 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
- 41
- 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
- Number of ways of writing n as a sum of 5 squares.at n=43A000132
- Jordan-Polya numbers: products of factorial numbers A000142.at n=48A001013
- Sorted list of orders of Weyl groups of types A_n, B_n, D_n, E_n, F_4, G_2.at n=15A001217
- a(n) = n!/6!.at n=4A001730
- a(n) = (2*n)!/(n+1)!.at n=5A001761
- Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=18A002182
- Superior highly composite numbers: positive integers n for which there is an e > 0 such that d(n)/n^e >= d(k)/k^e for all k > 1, where the function d(n) counts the divisors of n (A000005).at n=7A002201
- Expansion of (theta_3(z)*theta_3(7z)+theta_2(z)*theta_2(7z))^3.at n=30A002653
- Theta series of 6-dimensional lattice A_6^(2) (other names for this lattice or the corresponding quadratic form are LAMBDA_{3,lambda}, P_6^(5), phi_6, F_14).at n=30A002706
- Coefficients for extrapolation.at n=3A002738
- Smallest number with 2n divisors.at n=29A003680
- 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=18A004394
- Colossally abundant numbers: m for which there is a positive exponent epsilon such that sigma(m)/m^{1 + epsilon} >= sigma(k)/k^{1 + epsilon} for all k > 1, so that m attains the maximum value of sigma(m)/m^{1 + epsilon}.at n=7A004490
- Where records occur in A038548.at n=15A004778
- a(n) = n! if n is odd otherwise 0 (from the Taylor series for sin x).at n=7A005212
- Maximal period of an n-stage shift register.at n=12A005417
- Expansion of 6-dimensional cusp form (eta(q) * eta(q^3))^6 in powers of q.at n=46A007332
- An upper bound on the biplanar crossing number of the complete graph on n nodes.at n=35A007333
- Smallest k such that sigma(x) = k has exactly n solutions.at n=33A007368
- The minimal numbers: sequence A005179 arranged in increasing order.at n=31A007416