13697
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 26
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 13698
- 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
- 13696
- Möbius Function
- -1
- Radical
- 13697
- 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
- 151
- 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
- 1620
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Smallest k such that the smallest palindrome > k in the Reverse and Add! trajectory of k is reached after exactly n iterations.at n=37A015994
- Numbers k such that the continued fraction for sqrt(k) has period 37.at n=33A020376
- Primes of the form 36*n^2 - 810*n + 2753, n >= 0, sorted.at n=18A022464
- a(0) = 0. For n > 0, smallest non-palindromic number k such that the smallest palindrome in the Reverse and Add! trajectory of k is reached after exactly n iterations.at n=38A023109
- Least number of Reverse-then-add persistence n.at n=38A033866
- Primes whose consecutive digits differ by 2 or 3.at n=48A048414
- Primes of the form 36*k^2 - 810*k + 2753, listed in order of increasing parameter k >= 0.at n=18A050268
- Consider a room of size r X s where rs = 2n and 1 <= r <= s; count ways to arrange n Tatami mats in room; a(n) = total number of ways for all choices of r and s. Two arrangements are considered the same if one is a rotation or reflection of the other.at n=26A052270
- Primes of the form k(k+1)/2+2 (i.e., two more than a triangular number).at n=31A055472
- a(n) = 10*n^2 + 7.at n=37A061722
- Primes such that prime(p) +- pi(p) are simultaneously prime.at n=27A065117
- a(1) = 2, a(n+1) = smallest prime of the form a(n) + k*prime(n+1), k >1.at n=32A085041
- Primes which are the sum of three positive 4th powers.at n=23A085318
- Largest prime p for which every solution of the congruence x^n + y^n == z^n (mod p) is such that p divides x*y*z.at n=6A085749
- Number of decimal digits of Lucas(2^n).at n=16A094057
- a(1) = 3; for n > 1 a(n) is the least prime of form a(n-1) + k*prime(n-1) with k > 0.at n=33A095184
- Primes of the form x^2 + y^2 + z, where x, y and z are three successive numbers.at n=17A095697
- Let p = prime(sigma(n)) and q = prime(phi(n)), then p is in the sequence if p-q = 6.at n=19A103176
- Primes of the form 256n+129.at n=15A105130
- a(n) = 36*n^2 - 810*n + 2753, producing the conjectured record number of 45 primes in a contiguous range of n for quadratic polynomials, i.e., abs(a(n)) is prime for 0 <= n < 44.at n=32A117081