Number of the day: 5370

Properties of the number 5370:

5370 = 2 × 3 × 5 × 179 is the 4661^th composite number and is squarefree.
5370 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 1424 totatives.
5370 has an emirpimes digit sum 15 in base 10.
5370 has a triangular digit sum 15 in base 10.
5370 is the sum of 2 positive triangular numbers.
5370 is the difference of 2 positive pentagonal numbers in 1 way.
5370 is the difference of 2 positive pentagonal pyramidal numbers in 2 ways.
5370 = (60 × (3 × 60-1))/2 is a pentagonal number.
5370 = 4² + 5² + 73² is the sum of 3 positive squares.
5370² = 3222² + 4296² is the sum of 2 positive squares in 1 way.
5370² is the sum of 3 positive squares.
5370 is a proper divisor of 359² - 1.
5370 is palindromic in (at least) the following bases: 44, 59, -23, -61, and -91.
5370 in base 22 = b22 and consists of only the digits '2' and 'b'.
5370 in base 43 = 2cc and consists of only the digits '2' and 'c'.
5370 in base 44 = 2Y2 and consists of only the digits '2' and 'Y'.
5370 in base 58 = 1YY and consists of only the digits '1' and 'Y'.
5370 in base 59 = 1W1 and consists of only the digits '1' and 'W'.

The number 5370 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002625: Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
A014633: Even pentagonal numbers.
A049452: Pentagonal numbers with even index.
A196485: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,1,4 for x=0,1,2,3,4
A222604: Number of nX1 0..3 arrays with exactly floor(nX1/2) elements equal to at least one king-move neighbor, with new values introduced in row major 0..3 order
A222747: T(n,k)=Number of nXk 0..3 arrays with exactly floor(nXk/2) elements equal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..3 order
A226253: Number of ways of writing n as the sum of 9 triangular numbers.
A232696: E.g.f. A(x) satisfies: A'(x) = A(x/A'(x)) with A(0)=1.
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A263373: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.