Properties of the Number 83680

Eighty-Three Thousand Six Hundred Eighty

Basics

Value: 83679 → 83680 → 83681

Parity: even

Prime: No

Previous Prime: 83663

Next Prime: 83689

Digit Sum: 25

Digital Root: 7

Palindrome: No

Factorization: 2 ⁵ × 5 × 523

Divisors: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 10100011011100000

Octal: 243340

Duodecimal: 40514

Hexadecimal: 146e0

Square: 7002342400

Square Root: 289.2749557082327

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

T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2. A221400

Number T(n,k) of n-step walks on cubic lattice starting at (0,0,0), ending at (0,k,n-k), remaining in the first (nonnegative) octant and using steps (0,0,1), (0,1,0), (1,0,0), (-1,1,1), (1,-1,1), and (1,1,-1); triangle T(n,k), n>=0, 0<=k<=n, read by rows. A328300

Total number of even parts in the last section of the set of partitions of n. A206434

Number of bicolored acyclic graphs on n unlabeled nodes. A329053

Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2. A221401

Number of walks within N³ (the first octant of Z³) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 0), (1, -1, 0), (1, 1, 0), (1, 1, 1)}. A151022

Triangle read by rows: T(n,m) = 2·Eulerian(n, m-1) - (binomial(n-1, m-1) * binomial(n, m-1) / m)². A174160

O.g.f. A(x) satisfies: 0 = [xⁿ] exp( n*(n+1) * Integral 1/A(x) dx ) / A(x), for n > 0. A304862

Decimal expansion of (3/2)*log(3/2). A83680