amicable numbers | quadri-amicable number

An amicable quadruple as a quadruple (a, b, c, d) such that σ(a) = σ(b) = σ(c) = σ(d) = a + b + c + d, where σ(n) is the divisor function. If (a, b) and (x, y) are amicable pairs and GCD(a, x) = GCD(a, y) = GCD(b, x) = GCD(b, y) = 1, then (a x, a y, b x, b y) is an amicable quadruple. This follows from the identity σ(a x) = σ(a) σ(x) = (a + b)(x + y) = a x + a y + b x + b y. The smallest known amicable quadruple is (842448600, 936343800, 999426600, 1110817800).

amicable pair | amicable triple