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

### Properties of the number 8307:

8307 = 3^{2}× 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 = 19

^{2}+ … + 31

^{2}is the sum of at least 2 consecutive positive squares in 1 way.

8307 = 4154

^{2}- 4153

^{2}= 1386

^{2}- 1383

^{2}= 466

^{2}- 457

^{2}= 326

^{2}- 313

^{2}= 126

^{2}- 87

^{2}= 94

^{2}- 23

^{2}is the difference of 2 nonnegative squares in 6 ways.

8307 is the difference of 2 positive pentagonal numbers in 1 way.

8307 = 1

^{2}+ 5

^{2}+ 91

^{2}is the sum of 3 positive squares.

8307

^{2}= 3195

^{2}+ 7668

^{2}is the sum of 2 positive squares in 1 way.

8307

^{2}is the sum of 3 positive squares.

8307 is a proper divisor of 1279

^{4}- 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