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e-Divisor


d is called an e-divisor (or exponential divisor) of a number n with prime factorization

 n=p_1^(a_1)p_2^(a_2)...p_r^(a_r)

if d|n and

 d=p_1^(b_1)p_2^(b_2)...p_r^(b_r),

where b_j|a_j for 1<=j<=r. For example, the e-divisors of 36 are 2·3, 4·3, 2·9, and 4·9.


See also

e-Perfect Number

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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.Straus, E. G. and Subbarao, M. V. "On Exponential Divisors." Duke Math. J. 41, 465-471, 1974.

Referenced on Wolfram|Alpha

e-Divisor

Cite this as:

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

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