A029834 A discrete version of the Mangoldt function: if n is prime then floor(log(n)) else 0.

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

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: A198255 A290542 A359300 * 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