The aliquot divisors of n are the divisors of n less than n

Find two squares such that if each is increased by the sum of its aliquot divisors the resulting sums are equal.

for example,

16 has 5 divisors: 1, 2, 4, 8, 16

25 has 3 divisors: 1, 5, 25

(1 + 2 + 4 + 8) + 16 = (1 + 5) + 25 = 31

Find other pairs.

And, here’s a set of three squares having the same sum of divisors

The sum is, 133151753133

Find other sets

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For part a, pairs

4^2 & 5^2 Have sums of divisors = to 31

12^2 & 15^2 Have sums of divisors = to 403

28^2 & 35^2 Have sums of divisors = to 1767

36^2 & 45^2 Have sums of divisors = to 3751

44^2 & 55^2 Have sums of divisors = to 4123

52^2 & 65^2 Have sums of divisors = to 5673

68^2 & 85^2 Have sums of divisors = to 9517

76^2 & 95^2 Have sums of divisors = to 11811

84^2 & 105^2 Have sums of divisors = to 22971

92^2 & 115^2 Have sums of divisors = to 17143

108^2 & 135^2 Have sums of divisors = to 33883

116^2 & 145^2 Have sums of divisors = to 27001

124^2 & 155^2 Have sums of divisors = to 30783

132^2 & 165^2 Have sums of divisors = to 53599

148^2 & 185^2 Have sums of divisors = to 43617

156^2 & 195^2 Have sums of divisors = to 73749

For sets of 3

1284^2 & 1528^2 & 1605^2 Have sums of divisors = to 4657471

1628^2 & 1630^2 & 2035^2 Have sums of divisors = to 5801061

1956^2 & 2030^2 & 2445^2 Have sums of divisors = to 10773399

4884^2 & 4890^2 & 6105^2 Have sums of divisors = to 75413793

5064^2 & 6172^2 & 7715^2 Have sums of divisors = to 73854183

6216^2 & 7714^2 & 9291^2 Have sums of divisors = to 132408549

8988^2 & 10696^2 & 11235^2 Have sums of divisors = to 265475847

9768^2 & 12122^2 & 17441^2 Have sums of divisors = to 308953281

10360^2 & 12388^2 & 15485^2 Have sums of divisors = to 315743463

11396^2 & 11410^2 & 14245^2 Have sums of divisors = to 330660477

11836^2 & 14397^2 & 14795^2 Have sums of divisors = to 299457613

14124^2 & 16808^2 & 17655^2 Have sums of divisors = to 619443643

14652^2 & 14670^2 & 18315^2 Have sums of divisors = to 701928381

15544^2 & 15836^2 & 19795^2 Have sums of divisors = to 504081669

Paul.