Properties of the Number -684

Six Hundred Eighty-Four

Basics

Value: -685 → -684 → -683

Parity: even

Prime: No

Previous Prime:

Next Prime: 1

Digit Sum: 18

Digital Root: 9

Palindrome: No

Factorization: 2 ² × 3 ² × 19

Divisors: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: -1010101100

Octal: -1254

Duodecimal: -490

Hexadecimal: -2ac

Square: 467856

Square Root: 26.153393661244042

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

Alternating sum σ(1)-σ(2)+σ(3)-σ(4)+...+((-1)ⁿ⁺¹)*σ(n). A68762

Expansion of q^-1 * (φ(q) / φ(q⁹) - 1) / 2 in powers of q³ where φ() is a Ramanujan θ function. A128111

G.f.: A(x,q) = sqrt( Q(x,q) / Q(x,-q) ), where Q(x,q) = ∑_n=-oo..+oo (x - qⁿ)ⁿ. A292929

Expansion of η(q)² / (η(q²) * η(q⁴)⁶) in powers of q. A134414

Expansion of (χ(-x) / χ³(-x³))² in powers of·where χ() is a Ramanujan θ function. A216046

Expansion of r(q)³ / r(q³) in powers of q where r() is the Rogers-Ramanujan continued fraction. A285628

Row 3 in rectangular array A292929. A294066

Expansion of c(q²)² / (c(q) * c(q³)) in powers of q where c() is a cubic AGM θ function. A182034

Expansion of (1/q) * ((χ(q³) * χ(-q⁶)) / (χ(q) * χ(-q²)))⁴ in powers of q where χ() is a Ramanujan θ function. A193522

Expansion of ∏_k>0 theta₄(q^k)/theta₃(q^k), where theta₃() and theta₄() are the Jacobi θ functions. A320970