5357
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 20
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 5856
- Proper Divisor Sum (Aliquot Sum)
- 499
- 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
- 4860
- Möbius Function
- 1
- Radical
- 5357
- Omega Function (Ω)
- 2
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 28
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- Squarefree Number
- yes
- 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
- no
- Odd
- yes
Appears in sequences
- a(1) = 0, a(2) = -2; for n > 2, a(n) + a(n-2) - a(n-3) - a(n-5) - ... - a(n-p) = (-1)^(n+1)*n if n is prime, otherwise = 0, where p = largest prime < n.at n=45A002120
- Numbers k such that the continued fraction for sqrt(k) has period 50.at n=31A020389
- Numerators of continued fraction convergents to sqrt(122).at n=2A041220
- Least inverse of A048182.at n=26A048183
- Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 14.at n=29A050963
- a(n) = (9n^2 + 9n + 4)/2.at n=34A062123
- Frobenius number of the numerical semigroup generated by four consecutive tetrahedral numbers.at n=8A069761
- Trajectory of n under the Reverse and Add! operation carried out in base 4 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.at n=23A075421
- Number of compositions (ordered partitions) of n into parts 1, 2, and 5.at n=17A079971
- Members of A000124 which are multiples of 11.at n=18A083511
- a(n) = smallest k such that the base 4 Reverse and Add! trajectory of A075421(n) joins the trajectory of k.at n=23A091676
- Counterexamples to the conjecture that an even, prime-indexed triangular plus 1 equals a prime or that an odd, prime-indexed triangular minus 2 equals a prime.at n=6A097785
- Row sums of the triangle A097883.at n=21A098404
- a(n) is number of strings of length n that can be obtained by starting with abc and repeatedly doubling any substring in place and then discarding any string that contains two successive equal letters.at n=19A135017
- Numbers k such that A119682(k) is prime.at n=39A136682
- E.g.f.: A(x) = exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(x*A(x)^6*exp(...))))), an infinite power tower.at n=4A141363
- a(n) = floor(sqrt(2*n^5)).at n=27A172473
- Index of the smallest prime greater than (6n+1)^2.at n=38A174321
- a(n) = 8*n^2 - 2*n + 1.at n=26A185438
- Number of nX3 binary arrays without the pattern 0 1 0 vertically or horizontally.at n=4A188768