8144
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 17
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 10
- Divisor Sum
- 15810
- Proper Divisor Sum (Aliquot Sum)
- 7666
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 4064
- Möbius Function
- 0
- Radical
- 1018
- Omega Function (Ω)
- 5
- Little Omega Function (ω)
- 2
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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 52
- 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
- arctanh(cos(x)*arcsin(x))=x-12/5!*x^5-168/7!*x^7+8144/9!*x^9...at n=4A012489
- E.g.f.: log(sec(x) + arcsin(x)).at n=9A013195
- dot_product(n,n-1,...2,1)*(6,7,...,n,1,2,3,4,5).at n=26A026063
- Numerators of continued fraction convergents to sqrt(254).at n=5A041476
- Open 3-dimensional ball numbers (version 4): a(n) is the number of integer points (i,j,k) contained in an open ball of diameter n, centered at (1/2, 1/2, 1/2).at n=25A053596
- Smallest member of triple of consecutive numbers each of which is the sum of two different nonzero squares.at n=37A064715
- Lesser of three consecutive nonsquare integers each of which is the sum of two squares.at n=36A073412
- Triangle arising from (4,2) tennis ball problem, read by rows.at n=32A078990
- Triangular array related to tennis ball problem, read by rows.at n=53A079520
- Number of cousin primes < 10^n.at n=5A080840
- Trajectory of 63 under the map k -> A003415(k) (taking the arithmetic derivative).at n=11A090635
- a(n) = Sum_{k=1..9} a(n-k); a(8) = 1, a(n) = 0 for n < 8.at n=22A104144
- Number of 2 X 2 singular integer matrices with elements from {1,...,n}.at n=44A134506
- Binomial transform of A012245 (characteristic function of factorial numbers).at n=16A143963
- Number of prime parts in the last section of the set of partitions of n.at n=32A144120
- Number of cousin primes < 10^n.at n=5A152052
- If an array is made of columns of -nacci sequences, fibo-, tribo- etc. all starting w. 1,1,2 etc, the NW to SE diagonals can be extended by computation. The above is diagonal 7. See A159741 for details.at n=7A159743
- 2-comma numbers: n occurs in the sequence S[k+1] = S[k] + 10*last_digit(S[k-1]) + first_digit(S[k]) for two different splittings n=concat(S[0],S[1]).at n=41A166512
- a(n) = -1 + n + 4*n^2.at n=45A182868
- Expansion of -2*x^4 *(3*x^13 +2*x^12 +x^11 -6*x^10 -10*x^9 -6*x^8 +x^7 +7*x^6 +5*x^5 -x^4 -8*x^3 -11*x^2 -8*x -5) / ((x -1)^4 *(x +1)^2 *(x^2 +1)^2 *(x^2 +x +1)^2).at n=46A187397