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Primary Pseudoperfect Number

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

1/N+sum_(p|N)1/p=1

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

The similar equation

-1/N+sum_(p|N)1/p=1

arises in the definition of Giuga numbers.

See also

Giuga Number, Pseudoperfect Number

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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 sum_(p|N)1/p+1/N=1, Pseudoperfect Numbers, and Partially Weighted Graphs." Math. Comput. 69, 407-420, 1999.Cao, Z.; Liu, R.; and Zhang, L. "On the Equation sum_(j=1)^(s)(1/(x_j))+1/((x_1+...+x_n)) 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."

Referenced on Wolfram|Alpha

Primary Pseudoperfect Number

Cite this as:

Weisstein, Eric W. "Primary Pseudoperfect Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimaryPseudoperfectNumber.html

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