Number of the day: 5304

Properties of the number 5304:

5304 = 2³ × 3 × 13 × 17 is the 4600^th composite number and is not squarefree.
5304 has 4 distinct prime factors, 32 divisors, 8 antidivisors and 1536 totatives.
5304 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 5304 results in a sphenic number.
5304 = (16 × 17)/2 + … + (32 × 33)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
5304 = 1327² - 1325² = 665² - 661² = 445² - 439² = 227² - 215² = 115² - 89² = 95² - 61² = 77² - 25² = 73² - 5² is the difference of 2 nonnegative squares in 8 ways.
5304 is the sum of 2 positive triangular numbers.
5304 is the difference of 2 positive pentagonal numbers in 3 ways.
5304 = 2² + 20² + 70² is the sum of 3 positive squares.
5304² = 2496² + 4680² = 504² + 5280² = 3360² + 4104² = 2040² + 4896² is the sum of 2 positive squares in 4 ways.
5304² is the sum of 3 positive squares.
5304 is a proper divisor of 103² - 1.
5304 is palindromic in (at least) the following bases: 21, 77, and -21.
5304 in base 21 = c0c and consists of only the digits '0' and 'c'.
5304 in base 27 = 77c and consists of only the digits '7' and 'c'.
5304 in base 32 = 55o and consists of only the digits '5' and 'o'.
5304 in base 51 = 220 and consists of only the digits '0' and '2'.

The number 5304 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002421: Expansion of (1-4x)^(3/2) in powers of x.
A022264: a(n) = n*(7*n - 1)/2.
A032279: Number of bracelets (turn over necklaces) of n beads of 2 colors, 5 of them black.
A084921: LCM(p-1, p+1) where p is the n-th prime.
A085250: 4 times hexagonal numbers: a(n) = 4*n*(2*n-1).
A188992: T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 antidiagonally or horizontally
A225310: T(n,k)=Number of nXk -1,1 arrays such that the sum over i=1..n,j=1..k of i*x(i,j) is zero and rows are nondecreasing (ways to put k thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate)
A241435: T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4
A252615: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 8 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 8
A275090: T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.