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Abundancy
From OeisWiki
n 

abundancy (n) :=
,σ (n) n
σ (n) 
n 
Since

=σ (n) n
=d∑ d ∣nn ∑ d ∣n
,d n
an equivalent definition is

abundancy (n) := σ − 1(n) = ∑ d ∣n
n 
 {1, 3, 4, 7, 6, 2, 8, 15, 13, 9, 12, 7, 14, 12, 8, 31, 18, 13, 20, 21, 32, 18, 24, 5, 31, 21, 40, 2, 30, 12, 32, 63, 16, 27, 48, 91, 38, 30, 56, 9, 42, 16, 44, 21, 26, 36, 48, 31, ...}
n 
 {1, 2, 3, 4, 5, 1, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 6, 19, 10, 21, 11, 23, 2, 25, 13, 27, 1, 29, 5, 31, 32, 11, 17, 35, 36, 37, 19, 39, 4, 41, 7, 43, 11, 15, 23, 47, 12, 49, 50, ...}
Abundant numbers are numbers with abundancy greater than 2, perfect numbers are numbers with abundancy equal to 2 and deficient numbers are numbers with abundancy less than 2.
Multiplyperfect numbers
 Main article page: Multiplyperfect numbers
n 
k n, k ≥ 1, 
k 
A007691 Multiplyperfect numbers:
n 
σ (n) 
 {1, 6, 28, 120, 496, 672, 8128, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240, 1379454720, 1476304896, 8589869056, 14182439040, 31998395520, 43861478400, 51001180160, 66433720320, 137438691328, 153003540480, ...}

n 
σ (n) 
n 
 {1, 2, 2, 3, 2, 3, 2, 4, 4, 3, 4, 4, 2, 4, 4, 3, 4, 3, 2, 5, 5, 4, 3, 4, 2, 4, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 4, 4, 2, 5, 4, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 4, 5, 6, 5, 4, 4, 5, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 5, 6, 6, 5, 4, 4, 5, 4, 4, 5, 6, 5, 5, 4, 6, 4, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, ...}
See also
Notes
 ↑ Weisstein, Eric W., Abundancy, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/Abundancy.html]