9744
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 24
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 40
- Divisor Sum
- 29760
- Proper Divisor Sum (Aliquot Sum)
- 20016
- 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
- 2688
- Möbius Function
- 0
- Radical
- 1218
- 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
- 135
- 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) = floor( n*(n-1)*(n-2)/19 ).at n=58A011901
- a(n) = n*(19*n + 1)/2.at n=32A022277
- a(n) = 10^n - n^4.at n=4A024118
- Expansion of 1/((1-2x)(1-6x)(1-10x)(1-12x)).at n=3A028003
- Theta series of 8-dimensional strongly 6-modular lattice O(6) with minimal norm 3.at n=29A029720
- "BGK" (reversible, element, unlabeled) transform of 2,1,1,1,...at n=22A032062
- (-1)sigma perfect numbers: (-1)sigma(a) = m*a for some integer m, where if a = Product p(i)^r(i) then (-1)sigma(a) = Product_{i} (-1 + Sum_{s=1..r(i)} p(i)^s).at n=3A034094
- Triangle T(n,k) = k! * Stirling1(n,k), 1<=k<=n.at n=23A048594
- First element r of (-1)sigma sociable triple (r,s,t): s=(-1)sigma(r), t=(-1)sigma(s), r=(-1)sigma(t), where if x=Product p(i)^r(i), then (-1)sigma(x)=Product(-1+(Sum p(i)^s(i), s(i)=1 to r(i))).at n=19A049057
- Expansion of e.g.f.: -(log(1-x))^3.at n=7A052748
- A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of three complementary pairs of simple musical tones: 7/6 and 12/7, 6/5 and 5/3 and 7/5 and 10/7.at n=27A060529
- Numbers k such that sigma(x) = k has exactly 7 solutions.at n=39A060663
- a(n) = 12*n*(n-1).at n=29A064200
- Barriers for bigomega(n): numbers n such that, for all m < n, m + bigomega(m) <= n.at n=43A068597
- Coefficients of certain polynomials (rising powers).at n=25A075181
- Expansion of 1/(1+2*x^2-x^3).at n=25A077965
- a(n) = n*phi(n*phi(n)).at n=28A078774
- a(n) = floor(binomial(n+7,7)/binomial(n+3,3)).at n=48A084628
- Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.at n=59A085838
- Number of partitions of n-th partition number into partition numbers.at n=11A086209