sigma4792

Sigma4792 refers to the sum-of-divisors function evaluated at the integer 4792, in number theory notation often written as sigma(4792) or σ(4792). The sigma function, also called the divisor function, assigns to each positive integer n the sum of all positive divisors of n, including 1 and n itself. It is a multiplicative function used to study divisor structure and related arithmetic properties.

To compute sigma(4792), factor 4792 into primes: 4792 = 2^3 × 599, where 599 is prime. Using multiplicativity, sigma(4792) = sigma(2^3) × sigma(599). For a prime power, sigma(p^a) = 1 + p + p^2 + ... + p^a, giving sigma(2^3) = 1 + 2 + 4 + 8 = 15 and sigma(599) = 1 + 599 = 600. Therefore sigma(4792) = 15 × 600 = 9000.

The resulting value, 9000, indicates that 4792 is a deficient number, since sigma(4792) < 2·4792 (9000 < 9584). The ratio sigma(4792)/4792 is approximately 1.88. The study of sigma(n) values helps classify integers as deficient, perfect, or abundant and informs broader investigations in multiplicative number theory and algorithmic number theory.

See also: divisor function, sigma function, perfect number, deficient number, abundant number.