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
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
Programs
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Mathematica
Array[If[PrimeQ[#], Floor[Log[#]], 0] &, 80] (* Harvey P. Dale, Jul 24 2013 *)
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PARI
v=[]; for(n=1,150,v=concat(v, if(isprime(n),floor(log(n)),))); v
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PARI
A029834(n) = if(!isprime(n),0,floor(log(n))); \\ Antti Karttunen, Feb 06 2019
Extensions
More terms from Antti Karttunen, Feb 06 2019
Comments