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e-Perfect Number


A number n is called an e-perfect number if sigma_e(n)=2n, where sigma_e(n) is the sum of the e-Divisors of n. If m is squarefree, then sigma_e(m)=m. As a result, if n is e-perfect and m is squarefree with m_|_n, then mn is e-perfect.

The first few e-perfect numbers are 36, 180, 252, 396, 468, ... (OEIS A054979). There are no odd e-perfect numbers. The first few primitive e-perfect numbers are 36, 1800, 2700, 17424, ... (OEIS A054980).


See also

e-Divisor

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References

Guy, R. K. "Exponential-Perfect Numbers." §B17 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 73, 1994.Sloane, N. J. A. Sequences A054979 and A054980 in "The On-Line Encyclopedia of Integer Sequences."Subbarao, M. V. and Suryanarayan, D. "Exponential Perfect and Unitary Perfect Numbers." Not. Amer. Math. Soc. 18, 798, 1971.

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e-Perfect Number

Cite this as:

Weisstein, Eric W. "e-Perfect Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/e-PerfectNumber.html

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