Primary Pseudoperfect Number

An integer  which is a product of distinct primes and which satisfies

(Butske et al. 1999). The first few are 2, 6, 42, 1806, 47058, ... (OEIS A054377).

The similar equation

arises in the definition of Giuga numbers.

REFERENCES:

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. "Giuga's Conjecture on Primality." Amer. Math. Monthly 103, 40-50, 1996.

Butske, W.; Jaje, L. M.; and Mayernik, D. R. "The Equation , Pseudoperfect Numbers, and Partially Weighted Graphs." Math. Comput. 69, 407-420, 1999.

Cao, Z.; Liu, R.; and Zhang, L. "On the Equation  and Znám's Problem." J. Number Th. 27, 206-211, 1987.

Ke, Z. and Sun, Q. "On the Representation of 1 by Unit Fractions." Sichuan Daxue Xuebao 1, 13-29, 1964.

Sloane, N. J. A. Sequence A054377 in "The On-Line Encyclopedia of Integer Sequences."