90
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 9
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 12
- Divisor Sum
- 234
- Proper Divisor Sum (Aliquot Sum)
- 144
- 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
- 30
- 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
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 17
- 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
- yes
- Carmichael Number
- no
Names
- German
- neunzig· ordinal: neunzigste
- English
- ninety· ordinal: ninetieth
- Spanish
- noventa· ordinal: 90º
- French
- quatre-vingt-dix· ordinal: quatre-vingt-dixième
- Italian
- novanta· ordinal: 90º
- Latin
- nonaginta· ordinal: 90.
- Portuguese
- noventa· ordinal: 90º
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=43A000028
- Numbers that are not squares (or, the nonsquares).at n=80A000037
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=45A000052
- Numbers k such that (2k)^4 + 1 is prime.at n=26A000059
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=64A000062
- Numbers k such that k^4 + 1 is prime.at n=17A000068
- Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.at n=9A000092
- a(n) = n*(n+3)/2.at n=12A000096
- Number of transformation groups of order n.at n=49A000113
- Number of transformation groups of order n.at n=57A000113
- Number of ways of writing n as a sum of 5 squares.at n=4A000132
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=28A000134
- Expansion of e.g.f. exp(-x^4/4)/(1-x).at n=5A000138
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=55A000201
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=55A000202
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=39A000203
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=57A000203
- a(n) = 3*(2*n)!/((n+2)!*(n-1)!).at n=5A000245
- Essentially the same as A001611.at n=9A000381
- Stirling numbers of second kind S(n,3).at n=6A000392