14357
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 20
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 6
- Divisor Sum
- 16758
- Proper Divisor Sum (Aliquot Sum)
- 2401
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 12264
- Möbius Function
- 0
- Radical
- 2051
- Omega Function (Ω)
- 3
- Little Omega Function (ω)
- 2
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
- yes
- 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
- 71
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Indices of primes where largest gap occurs.at n=14A005669
- a(n)-th and (a(n)+1)-st primes are the first pair of primes that differ by exactly 2n; a(n) = -1 if no such pair of primes exists.at n=42A038664
- Largest k such that round(1/(sqrt(prime(k+1))-sqrt(prime(k)))) = n where prime(n) denotes the n-th prime (conjectured values).at n=8A078693
- Numbers where A080374 increases.at n=19A080376
- Values of k that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.at n=15A084976
- Indices of primes where nondecreasing gaps occur.at n=29A085500
- (Prime(prime(n))^2-1)/24.at n=26A092772
- Where the records (A098968) occur in A046930 (if initial term is 0 not 1).at n=22A098969
- First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.at n=27A103669
- Integers k such that ceiling(Pi^k) is prime.at n=7A111937
- Pentagonal numbers that are the sum of a nonzero pentagonal number and a nonzero square in at least one way.at n=35A134938
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=38A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=37A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=39A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=36A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=42A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=41A144309
- a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.at n=40A144309
- Greatest k for which the Andrica-like conjectural inequalities, prime(k+1)-prime(k)-(1/n)*sqrt(prime(k)) < 0, appear to fail, based on empirical evidence.at n=4A161623
- Numbers n with property that n^2 contains "1234" as a substring.at n=9A175464