e-Perfect Number
المؤلف:
Guy, R. K.
المصدر:
"Exponential-Perfect Numbers." §B17 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
23-11-2020
1071
e-Perfect Number
A number 
is called an 
-perfect number if 
, where 
is the sum of the e-Divisors of 
. If 
is squarefree, then 
. As a result, if 
is 
-perfect and 
is squarefree with 
, then 
is 
-perfect.
The first few 
-perfect numbers are 36, 180, 252, 396, 468, ... (OEIS A054979). There are no odd 
-perfect numbers. The first few primitive 
-perfect numbers are 36, 1800, 2700, 17424, ... (OEIS A054980).
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.
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
