Lambda function

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In number theory, the Lambda function is a function on positive integers which gives the exponent of the multiplicative group modulo that integer.

The value of λ on a prime power is:

  • if is an odd prime.

The value of λ on a general integer n with prime factorisation

is then

The value of λ(n) always divides the value of Euler's totient function φ(n): they are equal if and only if n has a primitive root.