223
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 7
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 224
- Proper Divisor Sum (Aliquot Sum)
- 1
- 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
- 222
- Möbius Function
- -1
- Radical
- 223
- 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
- 70
- Smith 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
- 48
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- zweihundertdreiundzwanzig· ordinal: zweihundertdreiundzwanzigste
- English
- two hundred twenty-three· ordinal: two hundred twenty-third
- Spanish
- doscientos veintitrés· ordinal: 223º
- French
- deux cent vingt-trois· ordinal: deux cent vingt-troisième
- Italian
- duecentoventitre· ordinal: 223º
- Latin
- ducenti viginti tres· ordinal: 223.
- Portuguese
- duzentos e vinte e três· ordinal: 223º
Appears in sequences
- Primes that divide at least one term in every Fibonacci sequence.at n=11A000057
- Primes and squares of primes.at n=53A000430
- Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.at n=45A000606
- Running time of Takeuchi function.at n=5A000651
- Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes.at n=61A000700
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=10A000921
- Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).at n=37A000945
- Lucky numbers.at n=43A000959
- Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.at n=16A000960
- Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).at n=62A000961
- n! never ends in this many 0's.at n=43A000966
- Primes with 3 as smallest primitive root.at n=10A001123
- Primes == +-1 (mod 8).at n=20A001132
- Primes p such that the multiplicative order of 2 modulo p is (p-1)/6.at n=1A001136
- a(n) = floor(n*log((14/11)*n^(10/9))).at n=48A001195
- Full reptend primes: primes with primitive root 10.at n=17A001913
- Beatty sequence of (5+sqrt(13))/2.at n=51A001956
- v-pile positions of the 4-Wythoff game with i=3.at n=42A001968
- Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence.at n=8A001970
- a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p).at n=38A002121