709
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 710
- 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
- 708
- Möbius Function
- -1
- Radical
- 709
- 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
- 33
- 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
- 127
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- siebenhundertneun· ordinal: siebenhundertneunste
- English
- seven hundred nine· ordinal: seven hundred ninth
- Spanish
- setecientos nueve· ordinal: 709º
- French
- sept cent neuf· ordinal: sept cent neufième
- Italian
- settecentonove· ordinal: 709º
- Latin
- septingenti novem· ordinal: 709.
- Portuguese
- setecentos e nove· ordinal: 709º
Appears in sequences
- Number of points of norm <= n^2 in square lattice.at n=15A000328
- Numbers that are not the sum of 4 tetrahedral numbers.at n=38A000797
- Primes p of the form 3k+1 such that Sum_{x=1..p} cos(2*Pi*x^3/p) > sqrt(p).at n=30A000921
- Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.at n=29A000960
- Primes with primitive root 2.at n=52A001122
- Number of partitions of n into at most 6 parts.at n=26A001402
- Full reptend primes: primes with primitive root 10.at n=45A001913
- From a Goldbach conjecture: records in A185091.at n=16A002092
- Numbers k such that (k^2 + k + 1)/21 is prime.at n=34A002644
- Number of partitions of n into parts 5k+1 or 5k+4.at n=46A003114
- Numbers that are the sum of 5 positive 4th powers.at n=46A003339
- Divisible only by primes congruent to 4 mod 5.at n=31A004618
- Class 4- primes (for definition see A005109).at n=13A005112
- Representation degeneracies for Neveu-Schwarz strings.at n=11A005302
- Primes of the form m^2 + 3m + 9, where m can be positive or negative.at n=11A005471
- Positions of remoteness 6 in Beans-Don't-Talk.at n=19A005694
- Prime-indexed primes: primes with prime subscripts.at n=30A006450
- From relations between Siegel theta series.at n=5A006476
- Emirps (primes whose reversal is a different prime).at n=21A006567
- Number of one-sided 4-dimensional polyominoes with n cells.at n=6A006760