### Properties of the number 2057:

2057 = 11^{2}× 17 is the 1746

^{th}composite number and is not squarefree.

2057 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 1760 totatives.

2057 has a semiprime digit sum 14 in base 10.

2057 = 1029

^{2}- 1028

^{2}= 99

^{2}- 88

^{2}= 69

^{2}- 52

^{2}is the difference of 2 nonnegative squares in 3 ways.

2057 is the difference of 2 positive pentagonal numbers in 3 ways.

2057 is the sum of 3 positive squares.

2057 = 11

^{2}+ 44

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

2057

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

2057 is a divisor of 727

^{4}- 1.

2057 is palindromic in (at least) the following bases: 19, and 26.

2057 in base 7 = 5666 and consists of only the digits '5' and '6'.

2057 in base 15 = 922 and consists of only the digits '2' and '9'.

2057 in base 18 = 665 and consists of only the digits '5' and '6'.

2057 in base 19 = 5d5 and consists of only the digits '5' and 'd'.

2057 in base 25 = 377 and consists of only the digits '3' and '7'.

2057 in base 26 = 313 and consists of only the digits '1' and '3'.

### The number 2057 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A005902: Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.

A048898: One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-1). Here the 2 (mod 5) numbers (except for n=0).

A051869: 17-gonal (or heptadecagonal) numbers: n(15n-13)/2.

A060354: The n-th n-gonal number.

A074996: Floor of concatenation of n, n+1, n+2, n+3, n+4, n+5 divided by 6.

A083706: 2^(n+1)+n-1.

A140675: a(n) = n*(3*n + 19)/2.

A145812: Odd positive integers a(n) such that for every odd integer m>1 there exists a unique representation of m as a sum of the form a(l)+2a(s)

A160172: T-toothpick sequence (see Comments lines for definition).

A250769: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction

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