Number of the day: 4057

Properties of the number 4057:

4057 is a cyclic number.
4057 is the 560^th prime.
4057 has 13 antidivisors and 4056 totatives.
4057 has sum of divisors equal to 4058 which is semiprime.
4057 = 2029² - 2028² is the difference of 2 nonnegative squares in 1 way.
4057 is the sum of 2 positive triangular numbers.
4057 is the difference of 2 positive pentagonal numbers in 1 way.
4057 = 24² + 59² is the sum of 2 positive squares in 1 way.
4057 = 4² + 21² + 60² is the sum of 3 positive squares.
4057² = 2832² + 2905² is the sum of 2 positive squares in 1 way.
4057² is the sum of 3 positive squares.
4057 is a proper divisor of 1409⁶ - 1.
4057 is an emirp in (at least) the following bases: 4, 7, 9, 13, 15, 19, 23, 24, 28, 34, 43, 45, 49, 50, 51, 57, 59, 61, 63, 64, 67, 68, 69, 73, 77, 81, 87, 89, 93, 94, 98, and 99.
4057 is palindromic in (at least) the following bases: 52, -12, -22, -25, and -78.
4057 in base 5 = 112212 and consists of only the digits '1' and '2'.
4057 in base 21 = 944 and consists of only the digits '4' and '9'.
4057 in base 22 = 889 and consists of only the digits '8' and '9'.
4057 in base 24 = 711 and consists of only the digits '1' and '7'.
4057 in base 51 = 1SS and consists of only the digits '1' and 'S'.
4057 in base 52 = 1Q1 and consists of only the digits '1' and 'Q'.

The number 4057 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A025019: Smallest prime in Goldbach partition of A025018(n).
A031934: Lower prime of a pair of consecutive primes having a difference of 16.
A045710: Primes with first digit 4.
A059245: Primes p such that x^13 = 2 has no solution mod p.
A098182: a(n) = 3*a(n-1) - a(n-2) + a(n-3), a(0)=1,a(1)=1,a(2)=3.
A104803: "Floor of hypotenuses": a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
A136065: Mother primes of order 6.
A200838: T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases
A212729: T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)
A216451: Numbers which are simultaneously of the form x^2+y^2, x^2+2y^2, x^2+3y^2, x^2+7y^2, all with x>0, y>0.