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A181121 As n increases, the reciprocal of a(n) = asymptotic fraction of positive integers whose longest string of consecutive divisors is A181062(n). 1
2, 3, 12, 15, 70, 840, 1260, 2772, 30030, 720720, 765765, 12932920, 243374040, 6692786100, 40156716600, 83181770100, 2406725881560, 144403552893600, 148414762696200, 5476504743489780, 224275908542914800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..21.

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).

EXAMPLE

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.

CROSSREFS

Sequence in context: A124486 A260908 A123761 * A333319 A047163 A046486

Adjacent sequences:  A181118 A181119 A181120 * A181122 A181123 A181124

KEYWORD

easy,nonn

AUTHOR

Matthew Vandermast, Oct 07 2010

STATUS

approved

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Last modified December 2 10:39 EST 2020. Contains 338876 sequences. (Running on oeis4.)