Upper Bounds on the Sum of Principal Divisors of an Integer

@inproceedings{Eggleton2007UpperBO,
  title={Upper Bounds on the Sum of Principal Divisors of an Integer},
  author={Roger B. Eggleton and WILLIAM P. GALVIN},
  year={2007}
}
A prime-power is any integer of the form p", where p is a prime and a is a positive integer. Two prime-powers are independent if they are powers of different primes. The Fundamental Theorem of Arithmetic amounts to the assertion that every positive integer N is the product of a unique set of independent prime-powers, which we call the principal divisors of N. For example, 3 and 4 are the principal divisors of 12, while 2, 5 and 9 are the principal divisors of 90. The case N = 1 fits this… CONTINUE READING