The arithmetic, geometric, harmonic and “tetra” means of two positive numbers , are respectively , , and . The sextuplet is a mean crowd when its entries are positive integers; it is primitive iff the greatest common divisor of its entries (equivalently and ) is 1. The operator
is an involution on (primitive) mean crowds. It is proved that is a primitive mean crowd if and only if and for some primitive Pythagorean triple .