81
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
- 5
- Divisor Sum
- 121
- Proper Divisor Sum (Aliquot Sum)
- 40
- 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
- 54
- Möbius Function
- 0
- Radical
- 3
- Omega Function (Ω)
- 4
- Little Omega Function (ω)
- 1
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- yes
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- yes
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 22
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- yes
- Achilles Number
- no
- Perfect Power
- yes
- Smooth Number
- yes
- Carmichael Number
- no
Names
- German
- einundachtzig· ordinal: einundachtzigste
- English
- eighty-one· ordinal: eighty-first
- Spanish
- ochenta y uno· ordinal: 81º
- French
- quatre-vingt-un· ordinal: quatre-vingt-unième
- Italian
- ottantuno· ordinal: 81º
- Latin
- octoginta unus· ordinal: 81.
- Portuguese
- oitenta e um· ordinal: 81º
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=38A000028
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=16A000052
- Local stops on New York City A line subway.at n=8A000054
- Odious numbers: numbers with an odd number of 1's in their binary expansion.at n=40A000069
- Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3 with a(0) = a(1) = 0 and a(2) = 1.at n=10A000073
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=25A000134
- Largest order of automorphism group of a tournament with n nodes.at n=8A000198
- Largest order of automorphism group of a tournament with n nodes.at n=9A000198
- Largest order of automorphism group of a tournament with n nodes.at n=10A000198
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=49A000202
- Take sum of squares of digits of previous term; start with 3.at n=2A000218
- 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); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).at n=8A000223
- Powers of 3: a(n) = 3^n.at n=4A000244
- Number of points of norm <= n^2 in square lattice.at n=5A000328
- Sums of three squares: numbers of the form x^2 + y^2 + z^2.at n=69A000378
- Hexanacci numbers with a(0) = ... = a(5) = 1.at n=10A000383
- Numbers that are the sum of three nonzero squares.at n=51A000408
- 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); A000092 gives values of n where |P(n)| sets a new record; sequence gives A(A000092(n)).at n=4A000413
- Numbers that are the sum of 4 nonzero squares.at n=65A000414
- Smallest nonnegative number that is the sum of 3 squares in exactly n ways.at n=3A000437