Unlucky 13

Number Theory Level pending

Every natural number can be written as the sum of squares of other natural numbers. Some numbers can we expressed multiple ways.

For example:

The number 5 can be written as the sum of the squares of 2 and 1. (4 + 1 = 5). Or it can be written as the sum of 1, 1, 1, 1, and 1 (1 + 1 + 1 + 1 + 1 = 5).


Including rearranging the numbers. (5 has 3 options, 4 & 1, 1 & 5, and 1, 1, 1, 1, & 1.) How many ways can you write the number 13? Make this \(A\).


What is \(A - 13\)?

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