Number of the day: 8307

Carl Ludwig Siegel was born on this day 121 years ago.

Properties of the number 8307:

8307 = 3² × 13 × 71 is the 7264^th composite number and is not squarefree.
8307 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 5040 totatives.
8307 = 19² + … + 31² is the sum of at least 2 consecutive positive squares in 1 way.
8307 = 4154² - 4153² = 1386² - 1383² = 466² - 457² = 326² - 313² = 126² - 87² = 94² - 23² is the difference of 2 nonnegative squares in 6 ways.
8307 is the difference of 2 positive pentagonal numbers in 1 way.
8307 = 1² + 5² + 91² is the sum of 3 positive squares.
8307² = 3195² + 7668² is the sum of 2 positive squares in 1 way.
8307² is the sum of 3 positive squares.
8307 is a proper divisor of 1279⁴ - 1.
8307 is palindromic in (at least) the following bases: 48, 55, and -26.
8307 in base 25 = d77 and consists of only the digits '7' and 'd'.
8307 in base 45 = 44R and consists of only the digits '4' and 'R'.
8307 in base 47 = 3ZZ and consists of only the digits '3' and 'Z'.
8307 in base 48 = 3T3 and consists of only the digits '3' and 'T'.
8307 in base 52 = 33d and consists of only the digits '3' and 'd'.
8307 in base 54 = 2jj and consists of only the digits '2' and 'j'.
8307 in base 55 = 2f2 and consists of only the digits '2' and 'f'.

The number 8307 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006875: Non-seed mu-atoms of period n in Mandelbrot set.
A022103: Fibonacci sequence beginning 1, 13.
A031431: Least term in period of continued fraction for sqrt(n) is 7.
A056078: Number of proper T_1-hypergraphs with 3 labeled nodes and n hyperedges.
A136376: a(n) = n*F(n) + (n-1)*F(n-1).
A157365: 49n^2 + 2n.
A218563: Numbers n such that n^2 + 1 is divisible by a 4th power.
A218564: Numbers n such that n^2 + 1 is divisible by a 5th power.
A241744: Number of partitions p of n such that (number of numbers in p of form 3k) = (number of numbers in p of form 3k+1).
A252407: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 2 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 2 3 4 6 or 7