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A029833
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A discrete version of the Mangoldt function: if n is prime then round(log(n)) else 0.
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5
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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
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OFFSET
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1,5
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COMMENTS
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The real Mangoldt function Lambda(n) is equal to log(n) if n is prime else 0.
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32.
P. Ribenboim, Algebraic Numbers, p. 44.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65539
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MATHEMATICA
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Table[If[PrimeQ[n], Round[Log[n]], 0], {n, 200}] (* Harvey P. Dale, Nov 25 2020 *)
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PROG
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(PARI) A029833(n) = if(!isprime(n), 0, round(log(n))); \\ Antti Karttunen, Feb 06 2019
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CROSSREFS
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Cf. A029832, A029834, A053821.
Sequence in context: A029834 A318715 A202385 * A050948 A282695 A292936
Adjacent sequences: A029830 A029831 A029832 * A029834 A029835 A029836
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Antti Karttunen, Feb 06 2019
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STATUS
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approved
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