991
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 19
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 992
- 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
- 990
- Möbius Function
- -1
- Radical
- 991
- 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
- 98
- Smith Number
- no
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
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 167
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- neunhunderteinundneunzig· ordinal: neunhunderteinundneunzigste
- English
- nine hundred ninety-one· ordinal: nine hundred ninety-first
- Spanish
- novecientos noventa y uno· ordinal: 991º
- French
- neuf cent quatre-vingt-onze· ordinal: neuf cent quatre-vingt-onzième
- Italian
- novecentonovantuno· ordinal: 991º
- Latin
- nongenti nonaginta unus· ordinal: 991.
- Portuguese
- novecentos e noventa e um· ordinal: 991º
Appears in sequences
- Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.at n=44A000124
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=41A000921
- Primes with 6 as smallest primitive root.at n=10A001125
- Artiads: the primes p == 1 (mod 5) for which Fibonacci((p-1)/5) is divisible by p.at n=7A001583
- Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.at n=53A001914
- Primes of the form k^2 - k - 1.at n=19A002327
- Quintan primes: p = (x^5 + y^5)/(x + y).at n=6A002650
- Numbers that are the sum of 11 positive 6th powers.at n=16A003367
- Nonsquare values of m in the discriminant D = 4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k>0} Kronecker(D,k)/k.at n=20A003421
- Absolute primes (or permutable primes): every permutation of the digits is a prime.at n=21A003459
- Primes written backwards.at n=45A004087
- Divisible only by primes congruent to 4 mod 7.at n=29A004622
- Numbers k such that 4!*(2k-5)!/(k!*(k-1)!) is an integer.at n=8A004784
- Numbers k such that 6!*(2*k-7)!/(k!*(k-1)!) is an integer.at n=3A004786
- Numbers k such that 7!*(2k-8)!/(k!*(k-1)!) is an integer.at n=3A004787
- Class 3- primes (for definition see A005109).at n=52A005111
- a(n) = floor(tau*a(n-1)) + floor(tau*a(n-2)) with a(0)=0 and a(1)=2.at n=9A005909
- Erroneous version of A016054.at n=5A006031
- Prime-indexed primes: primes with prime subscripts.at n=38A006450
- Emirps (primes whose reversal is a different prime).at n=35A006567