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A029832 A discrete version of the Mangoldt function: if n is prime then ceiling(log(n)) else 0. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A320535 A174479 A134269

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

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Last modified May 25 07:29 EDT 2020. Contains 334584 sequences. (Running on oeis4.)