Properties of the Number 2048

Two Thousand Forty-Eight

Basics

Value: 2047 → 2048 → 2049

Parity: even

Prime: No

Previous Prime: 2039

Next Prime: 2053

Digit Sum: 14

Digital Root: 5

Palindrome: No

Factorization: 2 ¹¹

Divisors: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Polygonal

Triangular: No

Square: No

Pentagonal: No

Hexagonal: No

Heptagonal: No

Tetrahedral: No

Today's Target

8509 Try Today's Challenge

Representations

Binary: 100000000000

Octal: 4000

Duodecimal: 1228

Hexadecimal: 800

Square: 4194304

Square Root: 45.254833995939045

Classification

Fibonacci: No

Bell Number: No

Factorial Number: No

Regular Number: Yes

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: Yes

Fermat Number: No

Cullen Number: No

OEIS Sequences

Powers of 2: a(n) = 2ⁿ. A79

Expansion of ∏_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts. A9

Coefficients of expansion of (1-x)/(1-2·x) in powers of x. A11782

Least integer of each prime signature A124832; also products of primorial numbers A002110. A25487

Unary-encoded compressed factorization of natural numbers. A156552

3-smooth numbers: numbers of the form 2ⁱ*3^j with i, j >= 0. A3586

Self-inverse permutation of the positive integers induced by partition enumeration in A112798 and partition conjugation. A122111

If n = p_i^e_i * ... * p_k^e_k, p_i < ... < p_k primes (with p_i = prime(i)), then a(n) = (1/2) * (e_i * 2ⁱ + ... + e_k * 2^k). A48675

a(n) = 2·n². A1105

1 and the prime powers p^m where m >= 2, thus excluding the primes. A25475