Niven's constant
In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H = 1 and H = the largest exponent appearing in the unique prime factorization of a natural number n > 1, then Niven's constant is given by
where ζ is the value of the Riemann zeta function at the point k.
In the same paper Niven also proved that
where h = 1, h = the smallest exponent appearing in the unique prime factorization of each natural number n > 1, o is little o notation, and the constant c is given by
and consequently that
