864
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
- 24
- Divisor Sum
- 2520
- Proper Divisor Sum (Aliquot Sum)
- 1656
- 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
- 288
- Möbius Function
- 0
- Radical
- 6
- Omega Function (Ω)
- 8
- Little Omega Function (ω)
- 2
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
- 116
- 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
- yes
- Achilles Number
- yes
- Perfect Power
- no
- Smooth Number
- yes
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Names
- German
- achthundertvierundsechzig· ordinal: achthundertvierundsechzigste
- English
- eight hundred sixty-four· ordinal: eight hundred sixty-fourth
- Spanish
- ochocientos sesenta y cuatro· ordinal: 864º
- French
- huit cent soixante-quatre· ordinal: huit cent soixante-quatrième
- Italian
- ottocentosessantaquattro· ordinal: 864º
- Latin
- octingenti sexaginta quattuor· ordinal: 864.
- Portuguese
- oitocentos e sessenta e quatro· ordinal: 864º
Appears in sequences
- Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.at n=38A000009
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=43A000114
- a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.at n=24A000423
- Jordan-Polya numbers: products of factorial numbers A000142.at n=29A001013
- Number of partitions of n into at most 4 parts.at n=45A001400
- Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).at n=48A001694
- Number of divisors of n-th highly composite number.at n=57A002183
- Numbers that are the sum of 10 positive 6th powers.at n=13A003366
- 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.at n=38A003586
- Theta series of D_4 lattice with respect to deep hole.at n=42A005879
- Highly powerful numbers: numbers with record value of the product of the exponents in prime factorization (A005361).at n=11A005934
- Number of entries in first n rows of Pascal's triangle not divisible by 3.at n=68A006048
- MU-numbers: next term is uniquely the product of 2 earlier terms.at n=15A007335
- Smallest k such that phi(x) = k has exactly n solutions, n>=2.at n=43A007374
- Jordan function J_2(n) (a generalization of phi(n)).at n=33A007434
- Jordan function J_2(n) (a generalization of phi(n)).at n=35A007434
- Frequency of n-th largest distance in N times N times N grid, N > n.at n=36A007544
- Numbers k such that phi(k) divides k.at n=32A007694
- Multiples of 18.at n=48A008600
- Multiples of 24.at n=36A008606