10223
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 8
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10224
- Proper Divisor Sum (Aliquot Sum)
- 1
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 10222
- Möbius Function
- -1
- Radical
- 10223
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
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
- 179
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1254
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Number of bipartite partitions.at n=15A002768
- Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.at n=6A003448
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (odd natural numbers), t = A000201 (lower Wythoff sequence).at n=32A024599
- Lower prime of a difference of 20 between consecutive primes.at n=15A031938
- Triangle: T(n,k), k<=n: commutative groupoids with a nontrivial symmetry with n elements and k idempotents.at n=19A038023
- Least prime in A031938 (lesser of primes differing by 20) whose distance to the next 20-twin is 6*n.at n=31A052359
- Coefficients of monic irreducible polynomials over GF(4) listed in lexicographic order.at n=35A058948
- Coefficients of monic primitive irreducible polynomials over GF(4) listed in lexicographic order.at n=21A058952
- a(n) is the least prime p, such that next_prime(2*p) - 2*p = 2*n - 1.at n=15A059846
- Primes that are each the sum of two, three, and four consecutive composite numbers.at n=15A060339
- Numbers k such that k*2^m+1 are composites for all exponents m in the range 0<=m<=k.at n=23A061153
- Primes whose sum of digits is 8.at n=33A062343
- Integers for which the smallest m in A040076 such that n*2^m+1 is prime (A050921) increases.at n=12A064699
- Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 2.at n=4A068167
- Least m such that A078142(m) gives the n-th prime, where A078142(n) is the sum of the differences of the distinct prime factors p of n and the next square larger than p.at n=41A073939
- a(2*n), a(2*n+1) is the smallest consecutive prime pairs with at least n distinct common decimal digits.at n=8A076491
- Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={1}.at n=13A080010
- Primes prime(k) such that prime(k)*k falls between twin primes.at n=10A080174
- Primes such that successive differences are distinct palindromes.at n=32A087582
- Primes of the form 2*n^2 + 2*n - 1.at n=25A098828