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."