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From varying Egyptian fraction equations we obtain generalizations of primarypseudoperfect numbers and Giuga numbers which we call prime power psuedoperfectnumbers and prime power Giuga numbers respectively. We show that a sequence ofAmarnath Murthy in the OEIS is a subsequence of the sequence of prime powerpsuedoperfect numbers. Prime factorization conditions sufficient to imply anumber is a prime power pseudoperfect number or a prime power Giuga number aregiven. The conditions on prime factorizations naturally give rise to ageneralization of Fermat primes which we call extended Fermat primes.

Egyptian Fractions and Prime Power Divisors