997
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 25
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 998
- 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
- 996
- Möbius Function
- -1
- Radical
- 997
- 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
- 49
- 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
- 168
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- neunhundertsiebenundneunzig· ordinal: neunhundertsiebenundneunzigste
- English
- nine hundred ninety-seven· ordinal: nine hundred ninety-seventh
- Spanish
- novecientos noventa y siete· ordinal: 997º
- French
- neuf cent quatre-vingt-dix-sept· ordinal: neuf cent quatre-vingt-dix-septième
- Italian
- novecentonovantasette· ordinal: 997º
- Latin
- nongenti nonaginta septem· ordinal: 997.
- Portuguese
- novecentos e noventa e sete· ordinal: 997º
Appears in sequences
- a(n) is the number of conjugacy classes in the alternating group A_n.at n=24A000702
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=42A000921
- Primes with 7 as smallest primitive root.at n=9A001126
- Primes p such that the multiplicative order of 2 modulo p is (p-1)/3.at n=13A001133
- Numbers k such that phi(2k+1) < phi(2k).at n=12A001837
- a(n) = n^3 - floor( n/3 ).at n=10A002901
- Number of partitions of n into parts 5k+2 or 5k+3.at n=54A003106
- Largest n-digit prime.at n=2A003618
- Class 4- primes (for definition see A005109).at n=21A005112
- Primes p such that 2p-1 is also prime.at n=34A005382
- Primes p such that (p+1)/2 is prime.at n=20A005383
- Odd numbers not of form p + 2^k (de Polignac numbers).at n=17A006285
- From relations between Siegel theta series.at n=6A006476
- Primes p such that 2^p - 1 has at most 2 prime factors.at n=50A006514
- Number of n-step spirals on hexagonal lattice.at n=10A006778
- Where the prime race among 7k+1, ..., 7k+6 changes leader.at n=7A007354
- Primes of the form 8k + 5.at n=42A007521
- Primes of the form 2*k^2 + 29.at n=22A007641
- Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.at n=10A007671
- Coordination sequence T1 for Zeolite Code AFY.at n=26A008029