Number of the day: 5193

Properties of the number 5193:

5193 = 3² × 577 is the 4501^th composite number and is not squarefree.
5193 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 3456 totatives.
5193 = 4³ + 6³ + 17³ is the sum of 3 positive cubes in 1 way.
5193 = 2597² - 2596² = 867² - 864² = 293² - 284² is the difference of 2 nonnegative squares in 3 ways.
5193 is the sum of 2 positive triangular numbers.
5193 is the difference of 2 positive pentagonal numbers in 1 way.
5193 = 3² + 72² is the sum of 2 positive squares in 1 way.
5193 = 2² + 17² + 70² is the sum of 3 positive squares.
5193² = 432² + 5175² is the sum of 2 positive squares in 1 way.
5193² is the sum of 3 positive squares.
5193 is a proper divisor of 1153² - 1.
5193 = '5' + '193' is the concatenation of 2 prime numbers.
5193 = '51' + '93' is the concatenation of 2 emirpimes.
5193 is palindromic in (at least) the following bases: 24, 59, -20, -24, and -88.
5193 in base 8 = 12111 and consists of only the digits '1' and '2'.
5193 in base 23 = 9ii and consists of only the digits '9' and 'i'.
5193 in base 24 = 909 and consists of only the digits '0' and '9'.
5193 in base 41 = 33R and consists of only the digits '3' and 'R'.
5193 in base 58 = 1VV and consists of only the digits '1' and 'V'.
5193 in base 59 = 1T1 and consists of only the digits '1' and 'T'.

The number 5193 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024836: a(n) = least m such that if r and s in {1/1, 1/4, 1/7, ..., 1/(3n-2)} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.
A050065: a(n) = a(n-1)+a(m), where m=2^(p+1)+2-n and 2^p<n-1<=2^(p+1), for n >= 4.
A101853: a(n) = n*(20+15*n+n^2)/6.
A116646: Number of doubletons in all partitions of n. By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses).
A151793: Partial sums of A151782.
A179088: Positive integers of the form (2*m^2+1)/11.
A209814: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having two distinct values, and new values 0..3 introduced in row major order
A212417: Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> acb <--> bac where a<b<c.
A274160: Number of real integers in n-th generation of tree T(i) defined in Comments.
A288852: Number T(n,k) of matchings of size k in the triangle graph of order n; triangle T(n,k), n>=0, 0<=k<=floor(n*(n+1)/4), read by rows.