10723
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 10724
- 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
- 10722
- Möbius Function
- -1
- Radical
- 10723
- 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
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1307
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n.at n=12A000638
- Primes that remain prime through 3 iterations of function f(x) = 8x + 9.at n=6A023295
- Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 56 ones.at n=24A031824
- Lucky numbers with smallest increasing gaps (upper terms).at n=19A031885
- Euclid-Mullin sequence (A000945) with initial value a(1)=11 instead of a(1)=2.at n=21A051309
- Primes p from A031924 such that A052180(primepi(p)) = 17.at n=12A052234
- Five-digit distinct-digit primes.at n=24A074671
- Bisection (odd part) of Chebyshev sequence with Diophantine property.at n=4A077244
- Combined Diophantine Chebyshev sequences A077246 and A077244.at n=9A077248
- Initial term in sequence of four consecutive primes whose consecutive differences have d-pattern = [6, 4, 6]; short d-string notation for pattern = [646].at n=18A078856
- 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=39A080437
- Class 6- primes (for definition see A005109).at n=25A081425
- Numbers k such that numerator of Bernoulli(2k) is divisible by the square of 59, the second irregular prime.at n=15A093058
- Initial members of 25 consecutive primes in a 5 X 5 spiral wherein the mean of all 12 sums is prime.at n=25A094458
- Primes p such that index of p, the sum of p's digits and the number of p's digits are all primes.at n=25A109982
- Primes prime(i) such that their sum-of-index-digits A007953(i) and their sum-of-digits A007605(i) are consecutive primes.at n=43A117460
- Numbers k such that 2^k, 3^k, 5^k, 7^k, 11^k, 13^k, 17^k and 19^k have even digit sum.at n=33A119897
- Primes of the form 7x^2+195y^2.at n=37A140018
- Primes of the form 210n + 13.at n=27A140841
- Primes congruent to 28 mod 31.at n=42A142032