1105 as Sum of Two Squares

Theorem
$1105$ can be expressed as the sum of two squares in more ways than any smaller integer:

Proof
Here is the source code of a program in Python that finds all positive integers up to $1105$ that can be written as a sum of two squares in more ways than any smaller positive integer:

import numpy as np   def two_sq_decomp_rich(n): bound = int(np.floor(np.sqrt(n))) count_of_two_sq_decomps = [] for i in range(2*(bound + 1)*(bound + 1)): count_of_two_sq_decomps.append(0) for i in range(bound+1): for j in range(i+1): count_of_two_sq_decomps[i*i+j*j] = count_of_two_sq_decomps[i*i+j*j] + 1 max_sq_decomps = 0 sq_decomp_rich_numbers = [] for i in range(n+1): if count_of_two_sq_decomps[i] > max_sq_decomps: max_sq_decomps = count_of_two_sq_decomps[i] sq_decomp_rich_numbers.append(i) return sq_decomp_rich_numbers print(two_sq_decomp_rich(1105))

Output: [0, 25, 325, 1105]

Try it online!