A polygonal number is the number of dots arranged in the shape of a regular polygon. For example, 15 is a triangular number because dots can be arranged in the shape of a triangle with rows of 1, 2, 3, 4, and 5 dots. The number 16 is a square number because dots can be arranged in four rows of four.
A Blum integer is a semiprime—that is, the product of two distinct primes—whose factors have the form 
for some integer k. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form with 
and 
.
for some integer k. The number 21 is a Blum integer because its two prime factors, 3 and 7, have the form with and . Recently JessicaR had occasion to point out the properties of the number 57 to me. She observed, among other things, that 57 is both a Blum integer (
) and an icosagonal (i.e., 20-gonal) number.
) and an icosagonal (i.e., 20-gonal) number. Write a function that takes as input a maximum value x and a number of sides n and returns the largest n-gonal number (i.e., polygonal number with n sides) that is a Blum integer. If there are no numbers in the range 1 to x that work, return y = [].
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