A029833 - OEIS

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

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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 *)