Properties of the Number -2688

Six Hundred Eighty-Eight

Basics

Value: -2689 → -2688 → -2687

Parity: even

Prime: No

Previous Prime:

Next Prime: 1

Digit Sum: 24

Digital Root: 6

Palindrome: No

Factorization: 2 ⁷ × 3 × 7

Divisors: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

Today's Target

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Representations

Binary: -101010000000

Octal: -5200

Duodecimal: -1680

Hexadecimal: -a80

Square: 7225344

Square Root: 51.84592558726288

Classification

Fibonacci: No

Bell Number: No

Factorial Number: No

Regular Number: No

Perfect Number: No

Special

Kaprekar Constant: No

Munchausen Constant: No

Armstrong Number: No

Kaprekar Number: No

Catalan Number: No

Vampire Number: No

Taxicab Number: No

Super Prime: No

Friedman Number: No

Fermat Number: No

Cullen Number: No

OEIS Sequences

Chebyshev coefficients of density of states of cubic lattice. A288458

T(n, k) = 2ⁿ * n! * [x^k] [zⁿ] (4·exp(x·z))/(exp(z) + 1)², triangle read by rows, for 0 <= k <= n. Coefficients of Euler polynomials of order 2. A326480

Triangle read by rows: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min(2i-1,2j-1) (A157454). A204021

Triangle read by rows, T(n,k) = (-1)^n-k*C(n,k)*kⁿ, for n >= 0 and 0 <= k <= n. A258773

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of {|i-j}, (A049581). A203993

G.f. A(x) satisfies: 3ⁿ - 1 = ∑_k=0..n [x^k]A(x)ⁿ and also satisfies: (3+z)ⁿ - (1+z)ⁿ + zⁿ = ∑_k=0..n [x^k](A(x)+z·x)ⁿ for all z, where [x^k]A(x)ⁿ denotes the coefficient of x^k in A(x)ⁿ. A100225

Riordan array ((3-sqrt(1+8x))/2, (sqrt(1+8x)-1)/4). A122440

Triangle T(n, k) = coefficients of p(n, x), where p(n, x) = (-1)ⁿ*(x+2-n)*(x+2)^n-1, p(0, x) = 1, and p(1, x) = -1-x, read by rows. A158285

arcsinh(arctan(x)*tan(x))=2/2!*x²+40/6!*x⁶-2688/8!*x⁸+210208/10!*x¹⁰... A12450

Triangle a(n,k) of the expansion coefficients of the Hermite polynomial 2·H(n/2,x) if n even, of H((n-1)/2,x)+H((n+1)/2,x) if n odd. A139158