### Properties of the number 5385:

5385 is a cyclic number.5385 = 3 × 5 × 359 is a sphenic number and squarefree.

5385 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 2864 totatives.

5385 has a semiprime digit sum 21 in base 10.

5385 has a Fibonacci digit sum 21 in base 10.

5385 has a triangular digit sum 21 in base 10.

5385 has an oblong digit product 600 in base 10.

Reversing the decimal digits of 5385 results in a sphenic number.

5385 = 8

^{2}+ … + 25

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

5385 = (30 × 31)/2 + … + (38 × 39)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.

5385 = 2693

^{2}- 2692

^{2}= 899

^{2}- 896

^{2}= 541

^{2}- 536

^{2}= 187

^{2}- 172

^{2}is the difference of 2 nonnegative squares in 4 ways.

5385 is the sum of 2 positive triangular numbers.

5385 is the difference of 2 positive pentagonal numbers in 2 ways.

5385 = 19

^{2}+ 20

^{2}+ 68

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

5385

^{2}= 3231

^{2}+ 4308

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

5385

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

5385 is a proper divisor of 719

^{2}- 1.

5385 is palindromic in (at least) the following bases: 24, 39, and -46.

5385 in base 24 = 989 and consists of only the digits '8' and '9'.

5385 in base 38 = 3RR and consists of only the digits '3' and 'R'.

5385 in base 39 = 3L3 and consists of only the digits '3' and 'L'.

### The number 5385 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A015617: Number of (unordered) triples of integers from [1,n] with no common factors between pairs.

A056219: Number of partitions of n in SPM(n): these are the partitions obtained from (n) by iteration of the following transformation: p -> p' if p' is a partition (i.e., decreasing) and p' is obtained from p by removing a unit from the i-th component of p and adding one to the (i+1)-th component, for any i.

A144698: Triangle of 4-Eulerian numbers.

A160353: Numbers of the form pqr, where p<q<r are odd primes such that r = +/-1 (mod pq).

A164578: Integers of the form (k+1)*(2k+1)/12.

A180839: T(n,k)=number of nXk arrays containing k indistinguishable copies of 1..n with rows and columns in lexicographically strictly increasing order

A187283: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 2X2 subblock sum equal to some diagonal or antidiagonal neighbor 2X2 subblock sum

A224690: T(n,k)=Number of (n+4)X(k+4) 0..1 matrices with each 5X5 subblock idempotent

A272782: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 533", based on the 5-celled von Neumann neighborhood.

A273707: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 873", based on the 5-celled von Neumann neighborhood.

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