10112
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 5
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 20400
- Proper Divisor Sum (Aliquot Sum)
- 10288
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 4992
- Möbius Function
- 0
- Radical
- 158
- Omega Function (Ω)
- 8
- 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
- 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
- E.g.f.: 2*exp(x)/(1-x)^3.at n=5A001340
- a(n) = Sum_{k=0..5} (n+k)! * C(5,k).at n=3A001347
- To get the 6th term, for example, note that 5th term has three (10 in ternary!) 1's, one (1) 0, etc., giving 10 1 1 0 1 2 2 1 1 2.at n=3A001389
- Expansion of exp(sinh(x)*sin(x)).at n=5A009232
- sinh(sinh(x)*sin(x))=2/2!*x^2+112/6!*x^6+10112/10!*x^10...at n=2A012528
- Duplicate of A012528.at n=2A024341
- Expansion of (theta_3(z)*theta_3(19z) + theta_2(z)*theta_2(19z))^4.at n=24A028644
- Differences between adjacent palindromic primes.at n=45A037010
- Numbers having three 1's in base 10.at n=39A043495
- Bessel function J_0(n) is a monotonically decreasing positive sequence.at n=23A046960
- Bessel function |J_0(n)| is a monotonically decreasing positive sequence.at n=43A046962
- a(n) * a(n)_reversed is a palindrome (and a(n) is not palindromic).at n=35A048344
- Numbers n such that sum of digits = number of digits.at n=35A061384
- a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n) when written in base 3. Display sequence in base 3.at n=43A063112
- Numbers k such that 10*k-1, 10*k-3, 10*k-7 and 10*k-9 are all prime.at n=37A064975
- Records in the Conway's alimentary function A070871.at n=45A070926
- Coefficient of q^1 in nu(n), where nu(0)=1, nu(1)=b and, for n >= 2, nu(n) = b*nu(n-1) + lambda*(1 + q + q^2 + ... + q^(n-2))*nu(n-2) with (b,lambda)=(2,2).at n=9A074358
- Binomial triangle based on factorials.at n=33A076571
- Sum of divisors of numbers containing in their decimal representation only the digits 0 and 1.at n=22A077810
- a(n) = {A081982(n)+1}/d, where d is the product of nonzero digits of A081982(n).at n=49A081987