### Properties of the number 5735:

5735 = 5 × 31 × 37 is a sphenic number and squarefree.5735 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 4320 totatives.

5735 has an oblong digit sum 20 in base 10.

5735 = 22

^{3}- 17

^{3}is the difference of 2 positive cubes in 1 way.

5735 = 2868

^{2}- 2867

^{2}= 576

^{2}- 571

^{2}= 108

^{2}- 77

^{2}= 96

^{2}- 59

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

5735 is the sum of 2 positive triangular numbers.

5735 is the difference of 2 positive pentagonal numbers in 2 ways.

5735 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.

5735 = (62 × (3 × 62-1))/2 is a pentagonal number.

5735 is not the sum of 3 positive squares.

5735

^{2}= 1860

^{2}+ 5425

^{2}= 1767

^{2}+ 5456

^{2}= 3224

^{2}+ 4743

^{2}= 3441

^{2}+ 4588

^{2}is the sum of 2 positive squares in 4 ways.

5735

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

5735 is a divisor of 211

^{3}- 1.

5735 = '57' + '35' is the concatenation of 2 semiprime numbers.

5735 is palindromic in (at least) the following bases: 49, 61, -19, -20, -25, -63, and -94.

5735 in base 9 = 7772 and consists of only the digits '2' and '7'.

5735 in base 11 = 4344 and consists of only the digits '3' and '4'.

5735 in base 19 = fgg and consists of only the digits 'f' and 'g'.

5735 in base 48 = 2NN and consists of only the digits '2' and 'N'.

5735 in base 49 = 2J2 and consists of only the digits '2' and 'J'.

5735 in base 53 = 22B and consists of only the digits '2' and 'B'.

5735 in base 60 = 1ZZ and consists of only the digits '1' and 'Z'.

5735 in base 61 = 1X1 and consists of only the digits '1' and 'X'.

### The number 5735 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A029552: Expansion of phi(x) / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.

A037277: Replace n by concatenation of its divisors >1.

A037284: Replace n by concatenation of its odd divisors >1.

A037285: Replace n by concatenation of its nontrivial odd divisors.

A049452: Pentagonal numbers with even index.

A138990: a(n) = Frobenius number for 4 successive primes = F[p(n),p(n+1),p(n+2),p(n+3)].

A185258: Side of triangle of the difference of pairs of triangular numbers whose sum and difference are triangular.

A202461: T(n,k)=Number of (n+2)X(k+2) binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column

A265065: Coordination sequence for (2,5,6) tiling of hyperbolic plane.

A271926: Denominator of (Prod(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1).

## No comments:

## Post a Comment