There are two four digit numbers that satisfy condition 1.
1458: sum digits is 18 and 18 ∙ 81 = 1458
1729: sum digits is 19 and 19 ∙ 91 = 1729.

But 1458 does not satisfy condition 2, so we delete it.
1729 does satisfy condition 2: 9271 = 73 ∙ 127 and
(73^2 + 127^2) / 2 = 10729.

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