A249226 Denominators of constants A(a) related to the asymptotic LCM of arithmetic progressions a*n+b (a and b coprime).

1, 1, 4, 3, 48, 5, 120, 105, 560, 63, 25200, 385, 332640, 19305, 64064, 45045, 11531520, 85085, 73513440, 2909907, 14780480, 6613425, 113809696, 37182145, 475931456, 386122275, 5949143200, 2151252675, 2248776129600, 215656441

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Steven Finch, Cilleruelo's LCM Constants, 2013. [Cached copy, with permission of the author]

Eric Weisstein's MathWorld, Dirichlet's theorem

Wikipedia, Dirichlet's theorem on arithmetic progressions

Index entries for sequences related to lcm's

Formula

A(a) = (a/phi(a))*Sum_{j=1..a, gcd(j,a)=1} 1/j.

log(lcm_{k=0..n} a*k+b) ~ A(a)*n for gcd(a,b)=1.

Example

Sequence A(a) begins 1, 2, 9/4, 8/3, 125/48, 18/5, 343/120, 352/105, 1863/560, ...

Mathematica

A[a_] := (a/EulerPhi[a])*Sum[If[GCD[j, a] == 1, 1/j, 0], {j, 1, a}]; Array[A, 40] // Denominator

Prog

(PARI) a(n)={denominator(n*sum(j=1, n, if(gcd(j, n)==1, 1/j))/eulerphi(n))} \\ Andrew Howroyd, Mar 16 2018

Crossrefs

Cf. A249225 (numerators).

Sequence in context: A016504 A362275 A324671 * A328193 A273878 A013335

Adjacent sequences: A249223 A249224 A249225 * A249227 A249228 A249229

Keyword

nonn,frac

Author

Jean-François Alcover, Oct 23 2014

Status

approved