It's important to understand that atomic number is a fundamental property of an element. It represents the number of protons in the nucleus of an atom, defining what element it is. Therefore, there isn't a concept of a "non-atomic number" in the same way that there isn't a concept of a "non-color" or a "non-shape."

However, you might be asking about things that relate to atoms but are not the atomic number:

* Mass number: This is the total number of protons and neutrons in an atom's nucleus. It can vary for the same element (isotopes).

* Number of neutrons: This is the difference between the mass number and the atomic number.

* Number of electrons: In a neutral atom, this is the same as the number of protons (the atomic number). However, atoms can gain or lose electrons, becoming ions with a different number of electrons than protons.

* Atomic weight: This is the average mass of all the isotopes of an element, taking into account their relative abundance.

These values, while related to atoms, are not the atomic number itself.