840
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 32
- Divisor Sum
- 2880
- Proper Divisor Sum (Aliquot Sum)
- 2040
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 192
- Möbius Function
- 0
- Radical
- 210
- Omega Function (Ω)
- 6
- Little Omega Function (ω)
- 4
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
- 41
- 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
- achthundertvierzig· ordinal: achthundertvierzigste
- English
- eight hundred forty· ordinal: eight hundred fortieth
- Spanish
- ochocientos cuarenta· ordinal: 840º
- French
- huit cent quarante· ordinal: huit cent quarantième
- Italian
- ottocentoquaranta· ordinal: 840º
- Latin
- octingenti quadraginta· ordinal: 840.
- Portuguese
- oitocentos e quarenta· ordinal: 840º
Appears in sequences
- Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.at n=19A000099
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=39A000114
- a(n) = (2*n+1)! / n!.at n=3A000407
- Invertible Boolean functions of n variables.at n=2A000723
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=23A000793
- Landau's function g(n): largest order of permutation of n elements. Equivalently, largest LCM of partitions of n.at n=24A000793
- Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).at n=61A000926
- a(n) = n! + (n-1)!.at n=5A001048
- Smallest even number that is an unordered sum of two odd primes in exactly n ways.at n=51A001172
- Number of Steiner triple systems (STS's) on 6n+1 or 6n+3 elements.at n=3A001201
- Number of degree-n permutations of order exactly 4.at n=6A001473
- Number of 3-line Latin rectangles.at n=4A001626
- a(n) = n!/6.at n=4A001715
- Highly abundant numbers: numbers k such that sigma(k) > sigma(m) for all m < k.at n=41A002093
- a(n) = LCM of denominators of Cotesian numbers {C(n,k), 0 <= k <= n}.at n=5A002176
- Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=14A002182
- 4-dimensional figurate numbers: a(n) = (6*n-2)*binomial(n+2,3)/4.at n=6A002419
- Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire that make use of n-th hole.at n=50A002491
- Number of different ways one can attack all squares on an n X n chessboard with the smallest number of non-attacking queens needed.at n=11A002568
- a(n) = n*phi(n).at n=34A002618