684
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 18
- Divisor Sum
- 1820
- Proper Divisor Sum (Aliquot Sum)
- 1136
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 216
- Möbius Function
- 0
- Radical
- 114
- 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
- 126
- Smith 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
Names
- German
- sechshundertvierundachtzig· ordinal: sechshundertvierundachtzigste
- English
- six hundred eighty-four· ordinal: six hundred eighty-fourth
- Spanish
- seiscientos ochenta y cuatro· ordinal: 684º
- French
- six cent quatre-vingt-quatre· ordinal: six cent quatre-vingt-quatrième
- Italian
- seicentoottantaquattro· ordinal: 684º
- Latin
- sescenti octoginta quattuor· ordinal: 684.
- Portuguese
- seiscentos e oitenta e quatro· ordinal: 684º
Appears in sequences
- a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).at n=15A000070
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=35A000114
- a(n) = number of solid (i.e., three-dimensional) partitions of n.at n=8A000293
- a(n) is the solution to the postage stamp problem with n denominations and 3 stamps.at n=18A001213
- a(n) = least value of m for which Liouville's function A002819(m) = -n.at n=28A002053
- 2nd differences are periodic.at n=19A002082
- a(n) = n*phi(n).at n=37A002618
- Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-18).at n=2A004419
- a(n) = floor(n*phi^9), where phi is the golden ratio, A001622.at n=9A004924
- a(n) = round(n*phi^9), where phi is the golden ratio, A001622.at n=9A004944
- a(n) = n! - n^2.at n=6A005008
- Number of entries in first n rows of Pascal's triangle not divisible by 3.at n=58A006048
- Switching classes of digraphs.at n=3A006536
- Number of polygons of length 4n on L-lattice.at n=7A006782
- Let S denote the palindromes in the language {0,1}*; a(n) = number of words of length n in the language SS.at n=11A007055
- Numbers k such that phi(x) = k has exactly 3 solutions.at n=27A007367
- Number of strict 3rd-order maximal independent sets in path graph.at n=30A007384
- Add 5, then reverse digits!.at n=36A007397
- Moebius transform of triangular numbers.at n=38A007438
- a(n) = floor(n^2/2).at n=37A007590