Abundance

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The abundance of a positive integer

n

is defined as

abundance (n) := σ (n) − 2 n,

where

σ (n)

is the sum of divisors of

n

.

Abundant numbers are numbers with abundance greater than 0, perfect numbers are numbers with abundance equal to 0 and deficient numbers are numbers with abundance less than 0.

A033880 Abundance of

n

, i.e.

σ (n)  −  2 n

.

{−1, −1, −2, −1, − 4, 0, − 6, −1, −5, −2, −10, 4, −12, − 4, − 6, −1, −16, 3, −18, 2, −10, −8, −22, 12, −19, −10, −14, 0, −28, 12, −30, −1, −18, −14, −22, 19, −36, −16, −22, 10, − 40, 12, − 42, − 4, −12, −20, − 46, 28, − 41, −7, −30, − 6, −52, 12, −38, 8, −34, −26, −58, 48, − 60, −28, −22, ...}

See also

• Abundancy

• Deficient numbers
• Perfect numbers
• Abundant numbers

• Multiperfect numbers (multiply-perfect numbers or k-perfect numbers)