83
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 84
- 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
- 82
- Möbius Function
- -1
- Radical
- 83
- 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
- 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
- no
- Narcissistic Number
- no
- Collatz Steps
- 110
- 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
- yes
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 23
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Names
- German
- dreiundachtzig· ordinal: dreiundachtzigste
- English
- eighty-three· ordinal: eighty-third
- Spanish
- ochenta y tres· ordinal: 83º
- French
- quatre-vingt-trois· ordinal: quatre-vingt-troisième
- Italian
- ottantatre· ordinal: 83º
- Latin
- octoginta tres· ordinal: 83.
- Portuguese
- oitenta e três· ordinal: 83º
Appears in sequences
- Number of positive integers <= 2^n of form x^2 + 16*y^2.at n=9A000018
- 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=39A000028
- Numbers that are not squares (or, the nonsquares).at n=73A000037
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=19A000052
- Primes that divide at least one term in every Fibonacci sequence.at n=6A000057
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=59A000062
- Number of odd integers <= 2^n of form x^2 + y^2.at n=8A000074
- Primes p == 3, 9, 11 (mod 20) such that 2p+1 is also prime.at n=4A000355
- Sums of three squares: numbers of the form x^2 + y^2 + z^2.at n=71A000378
- Numbers that are the sum of three nonzero squares.at n=53A000408
- Numbers that are the sum of 3 but no fewer nonzero squares.at n=33A000419
- Primes and squares of primes.at n=26A000430
- The greedy sequence of integers which avoids 3-term geometric progressions.at n=61A000452
- Number of partitions of n into distinct primes.at n=78A000586
- Number of nonnegative solutions of x^2 + y^2 = z in first n shells.at n=40A000592
- Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).at n=11A000601
- Landau's approximation to population of x^2 + y^2 <= 2^n.at n=8A000690
- n-th superior highly composite number A002201(n) is product of first n terms of this sequence.at n=38A000705
- a(n) = (n+2)*Catalan(n) - 1.at n=4A000777
- Total number of 1's in binary expansions of 0, ..., n.at n=33A000788