Number of the day: 8207

Edward Norton Lorenz was born on this day 100 years ago.

Properties of the number 8207:

8207 is a cyclic number.
8207 = 29 × 283 is semiprime and squarefree.
8207 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 7896 totatives.
8207 has an emirp digit sum 17 in base 10.
8207 = 4104² - 4103² = 156² - 127² is the difference of 2 nonnegative squares in 2 ways.
8207 is the difference of 2 positive pentagonal numbers in 2 ways.
8207 is not the sum of 3 positive squares.
8207² = 5660² + 5943² is the sum of 2 positive squares in 1 way.
8207² is the sum of 3 positive squares.
8207 is a proper divisor of 1699⁴ - 1.
8207 is an emirpimes in (at least) the following bases: 4, 8, 9, 15, 17, 20, 23, 24, 26, 27, 35, 39, 40, 41, 46, 49, 50, 52, 60, 65, 69, 70, 71, 72, 73, 75, 76, 78, 80, 85, 86, 87, 92, 93, 94, and 95.
8207 in base 40 = 557 and consists of only the digits '5' and '7'.

The number 8207 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052968: a(n) = 1 + 2^(n-1) + n for n > 0, a(0) = 2.
A066699: Numbers n such that binomial(2n,n)+1 is prime.
A074345: a(1) = 9; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A081691: From P-positions in a certain game.
A160379: Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160117 using cubes.
A164887: a(n) = smallest number that leads to a new fixed point under the base-2 Kaprekar map of A164884
A165778: Numbers n such that |2^n-57| is prime.
A190126: Numbers 1 through 10000 sorted lexicographically in binary representation.
A202849: Number of secondary structures of size n having no stacks of even length.
A251028: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements