10056
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 25200
- Proper Divisor Sum (Aliquot Sum)
- 15144
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3344
- Möbius Function
- 0
- Radical
- 2514
- Omega Function (Ω)
- 5
- Little Omega Function (ω)
- 3
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
- 42
- 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
- Positive numbers k such that k and 6*k are anagrams in base 7 (written in base 7).at n=1A023072
- Number of partitions of n such that cn(0,5) = cn(1,5) <= cn(2,5) = cn(4,5) <= cn(3,5).at n=67A036862
- Base-7 palindromes that start with 4.at n=25A043018
- Number of 2n-bead balanced binary strings, rotationally equivalent to reversed complement.at n=10A045655
- Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2.at n=18A065903
- Triangle T(n,k) (n >= 2, 1 <= k <= n-1) read by rows, where T(n,k) is the number of words of length n in the free group on three generators that require exactly k multiplications for their formation.at n=34A076262
- Expansion of theta_3(q) / theta_3(q^2) in powers of q.at n=37A080015
- G.f.: Product_{n >= 0} (1+x^(2n+1))/(1-x^(2n+1)).at n=37A080054
- a(n+1) -+ a(n) = prime, a(n+1)*a(n) = average of twin prime pairs, a(1)=1, a(2)=6.at n=31A154494
- E.g.f.: A(x) = exp( Sum_{n>=1} n(n+1)/2 * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1.at n=5A156325
- Number of n X n symmetric binary arrays with rows, considered as binary numbers, in nondecreasing order, and no more than 3 ones in any row.at n=6A162037
- Number of binary strings of length n with equal numbers of 00011 and 01100 substrings.at n=14A164231
- Triangle T(n, k) = coefficients of ( t(n, x) ) where t(n, x) = (1-x)^(n+1)*p(n, x)/x, p(n, x) = x*D( p(n-1, x) ), with p(1, x) = x/(1-x)^2, p(2, x) = x*(1+x)/(1-x)^3, and p(3, x) = x*(1+2*x+x^2)/(1-x)^4, read by rows.at n=38A166345
- Triangle T(n, k) = coefficients of ( t(n, x) ) where t(n, x) = (1-x)^(n+1)*p(n, x)/x, p(n, x) = x*D( p(n-1, x) ), with p(1, x) = x/(1-x)^2, p(2, x) = x*(1+x)/(1-x)^3, and p(3, x) = x*(1+2*x+x^2)/(1-x)^4, read by rows.at n=42A166345
- The row sums of triangle A167557.at n=4A167559
- Number of rhombuses on a (n+1)X8 grid.at n=38A190096
- Number of n X 2 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.at n=28A201975
- The Wiener index of the graph obtained by applying Mycielski's construction to the path graph on n vertices (n>=2).at n=40A228321
- Number of binary strings of length n having a cyclic shift that is a palindrome.at n=20A245582
- Smallest base b > 1 such that both prime(n) and prime(n+1) are base-b Wieferich primes, i.e., p = prime(n) satisfies b^(p-1) == 1 (mod p^2) and q = prime(n+1) satisfies b^(q-1) == 1 (mod q^2).at n=18A259075