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Srinivasa Ramanujan developed results in number theory, including the study of highly composite numbers: positive integers having more divisors than every smaller positive integer.^[ref]

His analysis connects record values of the divisor function with prime factorization. Prime exponents must be arranged in nonincreasing order as the primes increase: swapping an inverted pair would produce a smaller integer with the same divisor count, contradicting the record property. For example, $12=2^2\cdot 3$ has six positive divisors. The subject turns irregular arithmetic data into a constrained optimization problem.^[ref]