A181121 As n increases, the reciprocal of a(n) = asymptotic fraction of positive integers whose longest string of consecutive divisors is A181062(n).

2, 3, 12, 15, 70, 840, 1260, 2772, 30030, 720720, 765765, 12932920, 243374040, 6692786100, 40156716600, 83181770100, 2406725881560, 144403552893600, 148414762696200, 5476504743489780, 224275908542914800

Offset: 1

Author

Matthew Vandermast, Oct 07 2010

Keywords

• easy
• nonn

Comments

The asymptotic average, as n increases, of n's longest string of consecutive divisors is the constant 1.787780456..., given in A064859.

Examples

			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.
		

Formula

a(n) = A051451(n) * A025473(n+1)/(A025473(n+1)-1).

If A181062(n) = 2^(e-1), then a(n) = A003418(2^e) = A051451(n+1).