Dedekind Function

$$\psi(n)=n\prod_{\scriptstyle{\rm distinct\ prime}\atop\scriptstyle{\rm factors\ }p{\rm\ of\ }n} (1+p^{-1}),$$

where the Product is over the distinct Prime Factors of $n$. The first few values are 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, ... (Sloane's A001615).

See also Dedekind Eta Function, Euler Product, Totient Function

References

Cox, D. A. Primes of the Form $x^2 + n y^2$: 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 ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.