Yahoo Answers: Answers and Comments for Math question? [Mathematics]
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From Anonymous
enUS
Sun, 08 Dec 2019 10:02:56 +0000
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Yahoo Answers: Answers and Comments for Math question? [Mathematics]
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From Φ² = Φ+1: Well, 1300 is the sum of the squares of the po...
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Sun, 08 Dec 2019 11:05:18 +0000
Well, 1300 is the sum of the squares of the positive factors of 30. {1365 is the sum of the squares of the positive factors of 32 (being 2⁵), so it was going to be nearby}
The factors of 30² are 900, 450, 300, 225, 180, 150, 100, 90, 75, 60, 50, 45, 36, 30, 25, 20, 18, 15, 12, 10, 9, 6, 5, 4, 3, 2, and 1 which sum to 2821, so that checks out.
The square of the sum of the positive factors of 30 is (30 + 15 + 10 + 6 + 5 + 3 + 2 + 1)² which is 72² which is 5184.

From Krishnamurthy: The sum of the squares of the positive factors...
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Sun, 08 Dec 2019 14:39:15 +0000
The sum of the squares of the positive factors of a positive integer is 1300,
and the sum of the positive factors of the square of the integer is 2821.
Factorization:
1300 = 22 × 52 × 13
The square of the sum of the positive factors of the integer:
87^2 = 7569
Factorization:
2821 = 7 × 13 × 31
The square of the sum of the positive factors of the integer:
51^2 = 2601