617
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 618
- 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
- 616
- Möbius Function
- -1
- Radical
- 617
- 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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 131
- Smith Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- yes
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 113
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- sechshundertsiebzehn· ordinal: sechshundertsiebzehnste
- English
- six hundred seventeen· ordinal: six hundred seventeenth
- Spanish
- seiscientos diecisiete· ordinal: 617º
- French
- six cent dix-sept· ordinal: six cent dix-septième
- Italian
- seicentodiciassette· ordinal: 617º
- Latin
- sescenti septendecim· ordinal: 617.
- Portuguese
- seiscentos e dezessete· ordinal: 617º
Appears in sequences
- Number of partitions of n in which no parts are multiples of 3.at n=26A000726
- Boustrophedon transform of squares.at n=5A000745
- Numbers beginning with letter 's' in English.at n=41A000870
- Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.at n=37A000928
- Twin primes.at n=53A001097
- Primes with 3 as smallest primitive root.at n=26A001123
- Primes p such that the multiplicative order of 2 modulo p is (p-1)/4.at n=5A001134
- Lesser of twin primes.at n=27A001359
- Crystal ball sequence for hyperbolic tessellation 3^7 (from triangle group (2,3,7)).at n=5A001360
- Indices of prime Lucas numbers.at n=24A001606
- Numbers k such that phi(k+2) = phi(k) + 2.at n=43A001838
- Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).at n=20A001994
- Pythagorean primes: primes of the form 4*k + 1.at n=53A002144
- 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=54A002313
- Numbers that are the sum of 9 positive 5th powers.at n=23A003354
- Discriminants of real quadratic fields with narrow class number 1.at n=50A003655
- Numbers divisible only by primes congruent to 1 mod 7.at n=17A004619
- Numbers divisible only by primes congruent to 1 mod 8.at n=27A004625
- Class 4+ primes (for definition see A005105).at n=3A005108
- Class 3- primes (for definition see A005109).at n=31A005111