### Properties of the number 688:

688 = 2^{4}× 43 is the 563

^{th}composite number and is not squarefree.

688 has 2 distinct prime factors, 10 divisors, 15 antidivisors and 336 totatives.

688 has a semiprime digit sum 22 in base 10.

Reversing the decimal digits of 688 results in a semiprime.

688 = 173

^{2}- 171

^{2}= 88

^{2}- 84

^{2}= 47

^{2}- 39

^{2}is the difference of 2 nonnegative squares in 3 ways.

688 is the sum of 2 positive triangular numbers.

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

688 = 12

^{2}+ 12

^{2}+ 20

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

688

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

688 is a divisor of 257

^{2}- 1.

688 is palindromic in (at least) the following bases: 7, 12, 42, 85, and -11.

688 in base 3 = 221111 and consists of only the digits '1' and '2'.

688 in base 7 = 2002 and consists of only the digits '0' and '2'.

688 in base 9 = 844 and consists of only the digits '4' and '8'.

688 consists of only the digits '6' and '8'.

688 in base 12 = 494 and consists of only the digits '4' and '9'.

688 in base 18 = 224 and consists of only the digits '2' and '4'.

### The number 688 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A001743: Every digit contains at least one loop (version 1).

A006313: Numbers n such that n^16 + 1 is prime.

A008484: Number of partitions of n into parts >= 4.

A008598: Multiples of 16.

A014614: Numbers that are products of 5 primes (or 5-almost primes, a generalization of semiprimes).

A026797: Number of partitions of n in which the least part is 4.

A035607: Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d>=1, m >= 0).

A049600: Array T read by diagonals; T(i,j)=number of paths from (0,0) to (i,j) consisting of nonvertical segments (x(k),y(k))-to-(x(k+1),y(k+1)) such that 0=x(1)<x(2)<...<x(n-1)<x(n)=i, 0=y(1)<=y(2)<=...y(n-1)<=y(n)=j, for i >= 0, j >= 0.

A121028: Multiples of 8 containing a 8 in their decimal representation.

A178739: Product of the 4th power of a prime (A030514) and a different prime.

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