240
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 6
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 20
- Divisor Sum
- 744
- Proper Divisor Sum (Aliquot Sum)
- 504
- 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
- 64
- Möbius Function
- 0
- Radical
- 30
- Omega Function (Ω)
- 6
- 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
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 21
- 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
- yes
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Names
- German
- zweihundertvierzig· ordinal: zweihundertvierzigste
- English
- two hundred forty· ordinal: two hundred fortieth
- Spanish
- doscientos cuarenta· ordinal: 240º
- French
- deux cent quarante· ordinal: deux cent quarantième
- Italian
- duecentoquaranta· ordinal: 240º
- Latin
- ducenti quadraginta· ordinal: 240.
- Portuguese
- duzentos e quarenta· ordinal: 240º
Appears in sequences
- Number of ways of writing n as a sum of 4 squares; also theta series of four-dimensional cubic lattice Z^4.at n=29A000118
- Number of ways of writing n as a sum of 5 squares.at n=6A000132
- Number of 3-line Latin rectangles.at n=1A000536
- a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n > 3, with a(0)=a(1)=a(2)=0, a(3)=1.at n=10A000749
- a(n) = 4^n - C(4,3)*3^n + C(4,2)*2^n - C(4,1).at n=4A000919
- Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).at n=48A000926
- Numbers that are divisible by at least three different primes.at n=40A000977
- Jordan-Polya numbers: products of factorial numbers A000142.at n=19A001013
- Numbers that are the sum of 2 successive primes.at n=29A001043
- Dimensions (sorted, with duplicates removed) of real simple Lie algebras.at n=51A001066
- Maximal kissing number of an n-dimensional lattice.at n=8A001116
- Smallest even number that is an unordered sum of two odd primes in exactly n ways.at n=18A001172
- a(n) = floor(n*log((14/11)*n^(10/9))).at n=51A001195
- Double-bitters: only even length runs in binary expansion.at n=12A001196
- Numbers k such that phi(sigma(k)) = k.at n=5A001229
- Lah numbers: a(n) = (n-1)*n!/2.at n=3A001286
- Number of self-complementary Boolean functions of n variables, up to equivalence under the group (C_2)^n of all 2^n complementations of variables.at n=3A001320
- Maximal number of unattacked squares with n queens on n X n board (answers for n >= 17 only probable).at n=23A001366
- Number of n-node connected unicyclic graphs.at n=6A001429
- Expansion of {Product_{j>=1} (1 - (-x)^j) - 1}^12 in powers of x.at n=11A001490