gives the von Mangoldt function .
- MangoldtLambda is also know as von Mangoldt function.
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- MangoldtLambda[n] gives zero unless n is a prime power, in which case it gives the logarithm of the prime.
- For a positive integer n= p1k1⋯ pmkm with pi primes, MangoldtLambda[n] returns 0 unless m is equal to 1, in which case it gives Log[p1].
Examplesopen allclose all
Basic Examples (2)
Plot the MangoldtLambda sequence for the first 100 numbers:
Numerical Manipulation (3)
Basic Applications (3)
Properties & Relations (7)
MangoldtLambda gives zero except for prime powers:
MangoldtLambda is neither additive or multiplicative:
MangoldtLambda satisfies the identity :
MangoldtLambda satisfies the following identities: