MangoldtLambda—Wolfram Documentation

Examples

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Basic Examples (2)

Compute the Mangoldt function at :

Plot the MangoldtLambda sequence for the first 100 numbers:

Scope (8)

Numerical Evaluation (3)

Symbolic Manipulation (5)

Applications (5)

Basic Applications (3)

Highlight numbers n for which in black, and the prime bases of numbers n for which in red:

Compare MangoldtLambda sequence with logarithm function:

Plot the second Chebyshev function: [more info]

Demonstrate that it is asymptotic with :

Number Theory (2)

Use MangoldtLambda to test for a prime power:

Plot an approximation of the number of primes and prime powers using MangoldtLambda and ZetaZero:

The more zeros used, the closer the approximation:

Properties & Relations (7)

Neat Examples (3)

Wolfram Research (2008), MangoldtLambda, Wolfram Language function, https://reference.wolfram.com/language/ref/MangoldtLambda.html.

Text

Wolfram Research (2008), MangoldtLambda, Wolfram Language function, https://reference.wolfram.com/language/ref/MangoldtLambda.html.

CMS

Wolfram Language. 2008. "MangoldtLambda." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MangoldtLambda.html.

APA

Wolfram Language. (2008). MangoldtLambda. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MangoldtLambda.html

BibTeX

@misc{reference.wolfram_2025_mangoldtlambda, author="Wolfram Research", title="{MangoldtLambda}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/MangoldtLambda.html}", note=[Accessed: 23-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_mangoldtlambda, organization={Wolfram Research}, title={MangoldtLambda}, year={2008}, url={https://reference.wolfram.com/language/ref/MangoldtLambda.html}, note=[Accessed: 23-February-2026]}