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%I #23 Aug 29 2018 10:34:59
%S 2,6,5,70,7,231,858,1430,12155,46189,176358,676039,104006,44574,
%T 1077205,66786710,64822395,90751353,353452638,3829070245,134564468610,
%U 526024740930,2287064091,35830670759,71661341518,281132955186
%N 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.
%C 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.
%C 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.
%C Conjecture: a(n) always equals that lower bound. - _Don Reble_, Jul 01 2003
%e a(3) = (2*5*6)/(1*3*4) = 5. a(5) = (1*7*8*9*10)/(2*3*4*5*6) = 7.
%Y This is conjectured to be the same as A069113; they agree for at least the first 3400 terms.
%K nonn
%O 1,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003
%E More terms from _Ray Chandler_ and _Don Reble_, Jul 01 2003