Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, and particularly in number theory, a primary pseudoperfect number is a number N that satisfies the Egyptian fraction equation sum_{p|N}frac1p + frac1N = 1, where the sum is over only the prime divisors of N. Equivalently (as can be seen by multiplying this equation by N), sum_{p|N}frac{N}p + 1 = N. Except for the exceptional primary pseudoperfect number 2, this expression gives a representation for N as a sum of a set of distinct divisors of N; therefore each such number (except 2) is pseudoperfect. Primary pseudoperfect numbers were first investigated and named by Butske, Jaje, and Mayernik (2000). The first few primary pseudoperfect numbers are 2, 6, 42, 1806, 47058, 2214502422, 52495396602, ... (sequence A054377 in OEIS).

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