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Calculators/Maths/Amicable numbers check
Maths

Amicable numbers check calculator

Tests whether two numbers form an amicable pair: each is the sum of the other’s divisors.

What this calculator does

Amicable numbers check works out tests whether two numbers form an amicable pair: each is the sum of the other’s divisors. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

Formulas(a) = sum of proper divisors of a; amicable when s(a) = b and s(b) = a, with a ≠ b

The inputs explained

FieldWhat to enter
First numberA number. Starts at 220.
Second numberA number. Starts at 284.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with first number

Every other input is held at the calculator’s starting values while first number varies. Select any row to load that scenario into the calculator.

How the answer changes with first number
First numberAmicable pair?Sum of proper divisors of aSum of proper divisors of b
110No106 ≠ b220 ≠ a
165No123 ≠ b220 ≠ a
220Yes284 = b220 = a
330No534 ≠ b220 ≠ a
440No640 ≠ b220 ≠ a
660No1,356 ≠ b220 ≠ a