%I #2 Mar 30 2012 17:27:19
%S 2,3,12,15,70,840,1260,2772,30030,720720,765765,12932920,243374040,
%T 6692786100,40156716600,83181770100,2406725881560,144403552893600,
%U 148414762696200,5476504743489780,224275908542914800
%N As n increases, the reciprocal of a(n) = asymptotic fraction of positive integers whose longest string of consecutive divisors is A181062(n).
%C The asymptotic average, as n increases, of n's longest string of consecutive divisors is the constant 1.787780456..., given in A064859.
%F a(n) = A051451(n) * A025473(n+1)/(A025473(n+1)-1).
%F If A181062(n) = 2^(e-1), then a(n) = A003418(2^e) = A051451(n+1).
%e A number's longest string of consecutive divisors is a(5)=6 iff the integer is a multiple of 60 but not of 7. As n increases, the asymptotic fraction of positive integers satisfying those conditions equals 1/60 * 6/7 = 1/70. Therefore a(5) = 70.
%K easy,nonn
%O 1,1
%A _Matthew Vandermast_, Oct 07 2010