login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A249226
Denominators of constants A(a) related to the asymptotic LCM of arithmetic progressions a*n+b (a and b coprime).
2
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
Steven Finch, Cilleruelo's LCM Constants, 2013. [Cached copy, with permission of the author]
Eric Weisstein's MathWorld, Dirichlet's theorem
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
KEYWORD
nonn,frac
AUTHOR
STATUS
approved