10009
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 10
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10010
- 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
- 10008
- Möbius Function
- -1
- Radical
- 10009
- 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
- 166
- 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
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1231
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- a(n) = 5*a(n-1) - a(n-2), with a(1)=1, a(2)=4.at n=6A004253
- Primes that remain prime through 3 iterations of function f(x) = 3x + 2.at n=9A023277
- Primes that remain prime through 4 iterations of function f(x) = 3x + 2.at n=1A023307
- Primes that remain prime through 5 iterations of function f(x) = 3x + 2.at n=0A023335
- Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 66.at n=1A031654
- Numbers having three 0's in base 10.at n=17A043491
- Least n-digit 'happy' prime.at n=4A046519
- Sizes of successive balls in D_4 lattice.at n=32A046949
- Let prime(i) = i-th prime, let twin(n) = (P,Q) be n-th pair of twin primes; sequence gives prime(Q).at n=41A057473
- Numbers k such that k^2 contains only digits {0,1,8}, not ending with zero.at n=6A058421
- Primes p such that x^18 = 2 has no solution mod p, but x^6 = 2 has a solution mod p.at n=22A059664
- Primes p such that x^54 = 2 has no solution mod p, but x^6 = 2 has a solution mod p.at n=23A059665
- Number of partitions of n with zero crank.at n=50A064410
- Primes in which neighboring digits differ at most by 1.at n=41A068148
- Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. This is the prime sequence with the seed a(1) = 9.at n=4A068174
- Primes all of whose internal digits (if any) are 0.at n=54A069675
- Triangle read by rows in which row n gives n smallest n-digit primes.at n=11A073914
- 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=28A080437
- a(1) = 19, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n-1).at n=2A080442
- Primes p such that (r-p)/log(p) > 3, where r is the next prime after p.at n=27A082888