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

1,5

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

Mathematica

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

Prog

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

Crossrefs

Cf. A029832, A029834, A053821.

Sequence in context: A029834 A318715 A202385 * A050948 A282695 A292936

Adjacent sequences: A029830 A029831 A029832 * A029834 A029835 A029836

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Antti Karttunen, Feb 06 2019

Status

approved