A085057 a(n) is the smallest integer of the form a*b*c.../p*q*r..., where the numerator and the denominator contain n numbers each and a,b,c,...p,q,r... are all the integers from 1 to 2n.

2, 6, 5, 70, 7, 231, 858, 1430, 12155, 46189, 176358, 676039, 104006, 44574, 1077205, 66786710, 64822395, 90751353, 353452638, 3829070245, 134564468610, 526024740930, 2287064091, 35830670759, 71661341518, 281132955186

Offset

1,1

Comments

The largest value of the ratio is C(2n, n). a(4) = 70 is the smallest as well as the largest such integer. The smallest number can arise in more than one ways. i.e. a(3) = (2*5*6)/(1*3*4) = (3*4*5)/(1*2*6) = 5.

a(n) is bounded below by the squarefree part of (2n)! and above by C(2n, n). When those bounds are equal, that is a(n); for example, a(4) = 70. When a(n) equals that lower bound, it is fairly easy to compute. That happens for all of the first 3400 terms, anyway.

Conjecture: a(n) always equals that lower bound. - Don Reble, Jul 01 2003

Links

Table of n, a(n) for n=1..26.

Example

a(3) = (2*5*6)/(1*3*4) = 5. a(5) = (1*7*8*9*10)/(2*3*4*5*6) = 7.

Crossrefs

This is conjectured to be the same as A069113; they agree for at least the first 3400 terms.

Sequence in context: A343995 A358746 A175350 * A069113 A298329 A009462

Adjacent sequences: A085054 A085055 A085056 * A085058 A085059 A085060

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003

Extensions

More terms from Ray Chandler and Don Reble, Jul 01 2003

Status

approved