Properties of the Number 78592

Seventy-Eight Thousand Five Hundred Ninety-Two

Basics

Value: 78591 → 78592 → 78593

Parity: even

Prime: No

Previous Prime: 78583

Next Prime: 78593

Digit Sum: 31

Digital Root: 4

Palindrome: No

Factorization: 2 ⁸ × 307

Divisors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 307

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

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Representations

Binary: 10011001100000000

Octal: 231400

Duodecimal: 39594

Hexadecimal: 13300

Square: 6176702464

Square Root: 280.3426474869637

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

a(n) = ∑_k=0..n-1 binomial(n-1,k)*binomial(n+k,k). Also a(n) = T(n,n), array T as in A049600. A47781

a(n) = n²*(n⁶ + 28·n⁴ + 154·n² + 132)/315. A99195

Number of paths from (0,0) to the line x = n, each segment given by a vector (1,1), (1,-1), or (2,0), not crossing the x-axis, and including no horizontal segment on the x-axis. A247623

a(n) = 2·a(n-2) + 4·a(n-3), with initial terms 0, 1, 1. A134136

a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices {{-1, 1}, {0, -1}} [X] {{-1, 1}, {0, -1}} = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}. A138849

Array read by antidiagonals: the number of directed elements with area n on the lattice T_2k+1. A296129

Convolution of A055854 with A011782. A55855

Triangle read by rows: T(n,k) is the number of bicolored Dyck paths of semilength n and having k peaks of the form ud (0 <= k <= n). A bicolored Dyck path is a Dyck path in which each up-step is of two kinds: u and U. A114608

Triangle read by rows, T(n, k) = (-1)^n-k*binomial(n,k)*hypergeom([k - n, n + 1], k + 1, 2), for n >= 0 and 0 <= k <= n. A297898

Call two meanders from A005316 with 2n crossings equivalent if they differ by reflections in the X or Y axes. Sequence gives number of inequivalent meanders. A78592