Dedekind Function

The Dedekind -function is defined by the divisor product

(1)

where the product is over the distinct prime factors of , with the special case . The first few values are

			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)
			(9)
			(10)
			(11)

giving 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, ... (OEIS A001615).

Sums for  include

					(12)
					(13)

where  is the Möbius function.

The Dirichlet generating function is given by

			(14)
			(15)

where  is the Riemann zeta function.

REFERENCES:

Cox, D. A. Primes of the Form x2+ny2: Fermat, Class Field Theory and Complex Multiplication. New York: Wiley, p. 228, 1997.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 96, 1994.

Sloane, N. J. A. Sequence A001615/M2315 in "The On-Line Encyclopedia of Integer Sequences."