A029832 A discrete version of the Mangoldt function: if n is prime then ceiling(log(n)) else 0.

0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 3, 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, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 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. A029833, A029834, A053821.

Programs

Mathematica

Table[If[PrimeQ[n],Ceiling[Log[n]],0],{n,120}] (* Harvey P. Dale, Aug 23 2019 *)

PARI

A029832(n) = if(!isprime(n),0,ceil(log(n))); \\ Antti Karttunen, Feb 06 2019

Extensions

More terms from Antti Karttunen, Feb 06 2019