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

1,3

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

Prog

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

Crossrefs

Cf. A029833, A029834, A053821.

Sequence in context: A105118 A245359 A103271 * A361879 A320535 A174479

Adjacent sequences: A029829 A029830 A029831 * A029833 A029834 A029835

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Antti Karttunen, Feb 06 2019

Status

approved