A029833 A discrete version of the Mangoldt function: if n is prime then round(log(n)) else 0.

0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 5, 0, 0, 0, 5, 0, 5, 0, 0, 0, 5, 0, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The real Mangoldt function Lambda(n) is equal to log(n) if n is prime else 0.

References

• T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32.
• P. Ribenboim, Algebraic Numbers, p. 44.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65539

Crossrefs

Cf. A029832, A029834, A053821.

Programs

Mathematica

Table[If[PrimeQ[n],Round[Log[n]],0],{n,200}] (* Harvey P. Dale, Nov 25 2020 *)

PARI

A029833(n) = if(!isprime(n),0,round(log(n))); \\ Antti Karttunen, Feb 06 2019

Extensions

More terms from Antti Karttunen, Feb 06 2019