89
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 17
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 90
- Proper Divisor Sum (Aliquot Sum)
- 1
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 88
- Möbius Function
- -1
- Radical
- 89
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- yes
- 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
- no
- Narcissistic Number
- no
- Collatz Steps
- 30
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- yes
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 24
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Names
- German
- neunundachtzig· ordinal: neunundachtzigste
- English
- eighty-nine· ordinal: eighty-ninth
- Spanish
- ochenta y nueve· ordinal: 89º
- French
- quatre-vingt-neuf· ordinal: quatre-vingt-neufième
- Italian
- ottantanove· ordinal: 89º
- Latin
- octoginta novem· ordinal: 89.
- Portuguese
- oitenta e nove· ordinal: 89º
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=22A000009
- Coefficients of the 3rd-order mock theta function f(q).at n=29A000025
- 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=42A000028
- Numbers that are not squares (or, the nonsquares).at n=79A000037
- Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.at n=9A000043
- Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1) + a(n-2) - a(n-13).at n=11A000044
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=15A000052
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=63A000062
- a(n) = floor(n^(3/2)).at n=20A000093
- Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).at n=14A000199
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=54A000202
- A Beatty sequence: floor(n*(e-1)).at n=51A000210
- Take sum of squares of digits of previous term, starting with 2.at n=5A000216
- Take sum of squares of digits of previous term, starting with 2.at n=13A000216
- Take sum of squares of digits of previous term, starting with 2.at n=21A000216
- Take sum of squares of digits of previous term, starting with 2.at n=29A000216
- Take sum of squares of digits of previous term, starting with 2.at n=37A000216
- Take sum of squares of digits of previous term, starting with 2.at n=45A000216
- Take sum of squares of digits of previous term, starting with 2.at n=53A000216
- Take sum of squares of digits of previous term, starting with 2.at n=61A000216