Abundancy
المؤلف:
Guy, R. K.
المصدر:
"The Second Strong Law of Small Numbers." Math. Mag. 63
الجزء والصفحة:
...
21-11-2020
887
Abundancy
The abundancy of a number 
is defined as the ratio 
, where 
is the divisor function. For 
, 2, ..., the first few values are 1, 3/2, 4/3, 7/4, 6/5, 2, 8/7, 15/8, 13/9, 9/5, 12/11, 7/3, 14/13, ... (OEIS A017665 and A017666).
A positive integer 
for which 
is an integer is called a multiperfect number. The first few are 1, 6, 28, 120, 496, 672, 8128, ... (OEIS A007691), corresponding to the abundancies 1, 2, 2, 3, 2, 3, 2, 4, 4, ... (OEIS A054030).
REFERENCES:
Guy, R. K. "The Second Strong Law of Small Numbers." Math. Mag. 63, 3-20, 1990.
Sloane, N. J. A. Sequences A007691/M4182, A017665, A017666, and A054030 in "The On-Line Encyclopedia of Integer Sequences."
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