Properties of the Number 37680

Thirty-Seven Thousand Six Hundred Eighty

Basics

Value: 37679 → 37680 → 37681

Parity: even

Prime: No

Previous Prime: 37663

Next Prime: 37691

Digit Sum: 24

Digital Root: 6

Palindrome: No

Factorization: 2 ⁴ × 3 × 5 × 157

Divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 1001001100110000

Octal: 111460

Duodecimal: 19980

Hexadecimal: 9330

Square: 1419782400

Square Root: 194.11336893681485

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

Table T(n,k) is the number of n X (k+1) 0..1 arrays with every row least squares fitting to a positive-slope straight line and every column least squares fitting to a zero- or positive-slope straight line, with a single point array taken as having zero slope, read by downward antidiagonals. A222969

Expansion of 1/(1 - ∑_k>=0 x^3·k*(k+1/2+1)). A282502

Expansion of ∏_k>=1 ((1 - x^k)/(1 + x^k))^sigma₂(k). A320972

Weight multiplicities for the trivial representation of the Lie algebra E₈. A340522

Numbers n such that σ(n) is congruent to n mod φ(n). A66679

Number of compositions of n where differences between neighboring parts are in {-2,0,2}. A214253

a(n) is the number of different (n-1)-move routes for a king on an empty n X n chessboard. A355127

Smallest solution to x+n*φ(x) = σ(x) = x+n·A000010(x) = A000203(x). A76374

Triangle read by rows: T(n,k) = a(k)*binomial(n,k) (0 <= k <= n), where a(0)=1, a(1)=2, a(k) = a(k-1) + 3·a(k-2) for k >= 2 (a(k) = A006138(k)). A124959

Number of n X 5 0..1 arrays with every row least squares fitting to a positive-slope straight line and every column least squares fitting to a zero- or positive-slope straight line, with a single point array taken as having zero slope. A222966