I used to know someone who avoided perfect square numbers in self-picks because he thought they were unlucky. I'm not sure why, but that was his thing. He always made sure neither any of the individual numbers, nor the sum of all the numbers, nor the product of all the numbers was a perfect square.
For fun, I worked out a Venn diagram of this for Mega Millions tickets, under the current 5/70 + 1/25 matrix. The red circle is tickets where the sum of all six numbers is square, the green circle is tickets where the product of all six numbers is square, and the blue circle is tickets where at least one of the six individual numbers is square. Only 41.1206% of combinations manage to avoid square numbers in all three aspects.
This information is completely useless and will not help you win the lottery. When they change the matrix, it will be less than useless. But I thought I'd share it anyway.