317
domain: N
Properties
Digital Properties
- Digit Count
- 3
- 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
- 318
- 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
- 316
- Möbius Function
- -1
- Radical
- 317
- 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
- 37
- 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
- 66
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- dreihundertsiebzehn· ordinal: dreihundertsiebzehnste
- English
- three hundred seventeen· ordinal: three hundred seventeenth
- Spanish
- trescientos diecisiete· ordinal: 317º
- French
- trois cent dix-sept· ordinal: trois cent dix-septième
- Italian
- trecentodiciassette· ordinal: 317º
- Latin
- trecenti septendecim· ordinal: 317.
- Portuguese
- trezentos e dezessete· ordinal: 317º
Appears in sequences
- Number of points of norm <= n^2 in square lattice.at n=10A000328
- Boustrophedon transform of odd numbers.at n=5A000754
- Primes with primitive root 2.at n=26A001122
- Primes p such that the congruence 2^x == 3 (mod p) is solvable.at n=38A001915
- Primes p such that the congruence 2^x = 5 (mod p) is solvable.at n=35A001916
- From a Goldbach conjecture: records in A185091.at n=11A002092
- Pythagorean primes: primes of the form 4*k + 1.at n=30A002144
- Primes congruent to 1 or 2 modulo 4; or, primes of form x^2 + y^2; or, -1 is a square mod p.at n=31A002313
- Numbers k such that (k^2 + k + 1)/7 is prime.at n=32A002641
- Number of inequivalent n X n binary matrices, where equivalence means permutations of rows or columns.at n=4A002724
- a(n) = A001950(A003234(n)) + 1.at n=32A003249
- Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off the first, (M+1)st, (2M+1)st, (3M+1)st, etc. Repeat. The numbers that are left form the sequence.at n=52A003311
- a(1) = 3; for n>0, a(n+1) = a(n) + floor((a(n)-1)/2).at n=13A003312
- Inert rational primes in Q(sqrt(-5)).at n=34A003626
- Primes of the form 3n-1.at n=34A003627
- Primes congruent to {5, 7} mod 8.at n=34A003628
- Primes p == +- 3 (mod 8), or, primes p such that 2 is not a square mod p.at n=34A003629
- Inert rational primes in Q[sqrt(3)].at n=34A003630
- Primes congruent to 2 or 3 modulo 5.at n=35A003631
- Discriminants of quadratic fields whose fundamental unit has norm -1.at n=40A003653