84
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 12
- Divisor Sum
- 224
- Proper Divisor Sum (Aliquot Sum)
- 140
- 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
- 24
- Möbius Function
- 0
- Radical
- 42
- Omega Function (Ω)
- 4
- 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
- yes
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 9
- Smith Number
- no
Classification
- Natural
- yes
- Even
- yes
- Odd
- 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
Names
- German
- vierundachtzig· ordinal: vierundachtzigste
- English
- eighty-four· ordinal: eighty-fourth
- Spanish
- ochenta y cuatro· ordinal: 84º
- French
- quatre-vingt-quatre· ordinal: quatre-vingt-quatrième
- Italian
- ottantaquattro· ordinal: 84º
- Latin
- octoginta quattuor· ordinal: 84.
- Portuguese
- oitenta e quatro· ordinal: 84º
Appears in sequences
- Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.at n=40A000028
- Numbers that are not squares (or, the nonsquares).at n=74A000037
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=14A000052
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=60A000062
- Odious numbers: numbers with an odd number of 1's in their binary expansion.at n=42A000069
- Number of transformation groups of order n.at n=64A000113
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=11A000114
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=37A000115
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=26A000134
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=51A000201
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=51A000202
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=43A000203
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=64A000203
- A Beatty sequence: floor(n*(e-1)).at n=48A000210
- Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.at n=6A000237
- Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.at n=7A000292
- Number of partitions into non-integral powers.at n=3A000347
- Triangle of numbers related to triangle A049213; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497.at n=34A000369
- Numbers that are the sum of three nonzero squares.at n=54A000408
- Numbers that are the sum of 3 but no fewer nonzero squares.at n=34A000419