10709
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 17
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10710
- Proper Divisor Sum (Aliquot Sum)
- 1
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 10708
- Möbius Function
- -1
- Radical
- 10709
- 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
- 73
- Smith Number
- no
- Vampire 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
- yes
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1305
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- 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=1..oo} Kronecker(D,k)/k.at n=23A003420
- Numbers n such that n, 2n+1, and 4n+3 all prime.at n=43A007700
- Numbers k such that the continued fraction for sqrt(k) has period 65.at n=8A020404
- Primes that remain prime through 3 iterations of function f(x) = 5x + 4.at n=20A023284
- Denominators of continued fraction convergents to sqrt(806).at n=9A042555
- Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 21.at n=15A051962
- Primes p such that p^9 reversed is also prime.at n=32A059702
- Initial primes of Cunningham chains of first type with length exactly 3. Primes in A059453 that survive as primes just two "2p+1 iterations", forming chains of exactly 3 terms.at n=24A059762
- Smaller of twin primes whose middle term is a multiple of A002110(4)=210.at n=13A060230
- Append more digits to the n-th prime (leading zeros are permitted) until another prime is reached.at n=27A064792
- Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 5.at n=18A075585
- Primes p such that (3*p)^2 + p^2 + 3^2 and (3*p)^2 - p^2 - 3^2 are both prime.at n=29A079796
- For n < 5, a(n) = n-th prime. For n >= 5, let m = n-th prime. If m is a k-digit prime then a(n) = smallest prime obtained by inserting at least one digit between every pair of digits of m. There are (k-1) places where digit insertion takes place and a(n) contains at least 2k-1 digits.at n=40A080437
- a(n) = (n^3 + 24*n^2 + 65*n + 36)/6.at n=33A087863
- Table read by rows where row n contains lower twin primes of the form k*A002110(n)-1 in the range 0 < k < A006094(n+1).at n=49A088328
- Primes in A051022.at n=27A092908
- Interpolate 0's between each pair of digits of n-th prime.at n=40A092909
- Primes A005382(n) + A005384(n) - 1 with a twin prime A005382(n) + A005384(n) + 1.at n=17A099109
- Indices of prime generalized tetranacci numbers, A073817.at n=24A104577
- Highly cototient numbers that are prime, or intersection of A000040 and A100827.at n=30A105440