Dedekind psi function

The Dedekind ψ - function is a named after Richard Dedekind of several number-theoretic functions. Is a multiplicative function, it is by

Defined. The product extends over all prime divisors of

Values

By definition, the empty product is

For the next two natural numbers yields:

The sequence of function values ​​continues with 6, 6, 12, 8, 12, 12, 18, 12, 24, ....

Properties

  • The ψ function takes only positive integers as values ​​. For all sufficiently large is greater than and just:
  • For primes applies:
  • The ψ - function can also be
  • The Riemann zeta - function is:
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