7560
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 64
- Divisor Sum
- 28800
- Proper Divisor Sum (Aliquot Sum)
- 21240
- 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
- 1728
- Möbius Function
- 0
- Radical
- 210
- Omega Function (Ω)
- 8
- 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
- 39
- 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
- Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=19A002182
- Smallest number with 2n divisors.at n=31A003680
- Expansion of theta series of {E_7}* lattice in powers of q^(1/2).at n=20A003781
- Expansion of theta series of E_7 lattice in powers of q^2.at n=5A004008
- Where records occur in A038548.at n=16A004778
- Number of walks on square lattice. Column y=2 of A052174.at n=7A005560
- Unitary harmonic numbers (those for which the unitary harmonic mean is an integer).at n=10A006086
- Number of connected labeled 2-regular digraphs with n nodes.at n=6A007108
- The minimal numbers: sequence A005179 arranged in increasing order.at n=36A007416
- Theta series of {D_7}* lattice.at n=44A008423
- Theta series of A_5 lattice.at n=35A008445
- Number of ways of writing n as a sum of 7 squares.at n=11A008451
- Area of more than one Pythagorean triangle.at n=9A009127
- a(n) = floor( n*(n-1)*(n-2)/22 ).at n=56A011904
- a(n) = floor(n(n-1)(n-2)(n-3)/19).at n=21A011929
- tan(arctanh(x)-log(x+1)) = 1/2!*x^2 + 6/4!*x^4 + 150/6!*x^6 + 7560/8!*x^8...at n=4A013296
- E.g.f.: arctanh(arctanh(x)-log(x+1)).at n=4A013301
- Triangle of coefficients in expansion of (1+6x)^n.at n=31A013613
- Cycle class sequence c(n) (the number of true cycles of length n in which a certain node is included) for zeolite RTE = RUB-3 [Si24O48].2R starting with a T2 atom.at n=12A019224
- Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives triangle of numbers f(n,k)/n.at n=24A019576