A029832 - OEIS

%I #11 Aug 23 2019 16:16:59

%S 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,

%T 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,

%U 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

%N A discrete version of the Mangoldt function: if n is prime then ceiling(log(n)) else 0.

%C The real Mangoldt function Lambda(n) is equal to log(n) if n is prime else 0.

%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32.

%D P. Ribenboim, Algebraic Numbers, p. 44.

%H Antti Karttunen, <a href="/A029832/b029832.txt">Table of n, a(n) for n = 1..65539</a>

%t Table[If[PrimeQ[n],Ceiling[Log[n]],0],{n,120}] (* _Harvey P. Dale_, Aug 23 2019 *)

%o (PARI) A029832(n) = if(!isprime(n),0,ceil(log(n))); \\ _Antti Karttunen_, Feb 06 2019

%Y Cf. A029833, A029834, A053821.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_.

%E More terms from _Antti Karttunen_, Feb 06 2019