This is what I should have written:
I’d say the Lagarias criterion is in the same vein as Gronwall’s Theorem as well as Robin’s inequality and Robin’s Theorem (after Guy Robin, 1984).
Reference: Wikipedia article on Jeffrey Lagarias, at
http://en.wikipedia.org/wiki/Jeffrey_Lagarias#Career
Using arrays (vectors) in PARI/gp containing the prime exponents of a number for the (say) first 50,000 prime numbers, it’s quite easy to compute directly arithmetic functions such as sigma, the sum of divisors function. Thus, rather than work with plain integers types, I make it easier computationally on PARI/gp and my computer by working with vectors of the prime exponents in the unique factorization of a number into primes. For abundant numbers, I’m content to use only the first 50,000 primes for now.
