A029832 -id:A029832 - cp's OEIS frontend

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

N. J. A. Sloane

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

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32.
Paulo Ribenboim, Algebraic Numbers, p. 44.

Antti Karttunen, Table of n, a(n) for n = 1..65539

Cf. A029832, A029833, A053821, A062950.

Array[If[PrimeQ[#], Floor[Log[#]], 0] &, 80] (* Harvey P. Dale, Jul 24 2013 *)

v=[]; for(n=1,150,v=concat(v, if(isprime(n),floor(log(n)),))); v

A029834(n) = if(!isprime(n),0,floor(log(n))); \\ Antti Karttunen, Feb 06 2019

More terms from Antti Karttunen, Feb 06 2019

A029833 A discrete version of the Mangoldt function: if n is prime then round(log(n)) else 0.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 32.
P. Ribenboim, Algebraic Numbers, p. 44.

Antti Karttunen, Table of n, a(n) for n = 1..65539

Cf. A029832, A029834, A053821.

Table[If[PrimeQ[n],Round[Log[n]],0],{n,200}] (* Harvey P. Dale, Nov 25 2020 *)

A029833(n) = if(!isprime(n),0,round(log(n))); \\ Antti Karttunen, Feb 06 2019

More terms from Antti Karttunen, Feb 06 2019

A063529 a(n) = M(2^n-1), where M() is A029834, a discrete version of the Mangoldt function: if n is prime then floor(log(n)) else 0 and 2^n-1 is A000225.

Original entry on oeis.org

0, 1, 1, 0, 3, 0, 4, 0, 0, 0, 0, 0, 9, 0, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Jason Earls, Aug 01 2001

Cf. A029832, A029833, A053821, A062590, A029834, A000225.

j=[]; for(n=1,150,j=concat(j, if(isprime(2^n-1),floor(log(2^n-1)),))); j

cp's OEIS Frontend

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

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A029833 A discrete version of the Mangoldt function: if n is prime then round(log(n)) else 0.

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Author

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Comments

References

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A063529 a(n) = M(2^n-1), where M() is A029834, a discrete version of the Mangoldt function: if n is prime then floor(log(n)) else 0 and 2^n-1 is A000225.

Views

Author

Keywords

Crossrefs

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PARI