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A029834 A discrete version of the Mangoldt function: if n is prime then floor(log(n)) else 0. 6
0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 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, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

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.

Paulo Ribenboim, Algebraic Numbers, p. 44.

LINKS

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

MATHEMATICA

Array[If[PrimeQ[#], Floor[Log[#]], 0] &, 80] (* Harvey P. Dale, Jul 24 2013 *)

PROG

(PARI) v=[]; for(n=1, 150, v=concat(v, if(isprime(n), floor(log(n)), ))); v

(PARI) A029834(n) = if(!isprime(n), 0, floor(log(n))); \\ Antti Karttunen, Feb 06 2019

CROSSREFS

Cf. A029832, A029833, A053821, A062950.

Sequence in context: A197629 A198255 A290542 * A318715 A202385 A029833

Adjacent sequences:  A029831 A029832 A029833 * A029835 A029836 A029837

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 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)