Least non-border binomial coefficient having n prime factors, or 0 if none exists.
0, 6, 66, 210, 3570, 53130, 930930, 13123110, 1722580860, 29248649430, 265257422430, 81964543530870, 733629525258630
1
The first 10^8 rows of binomial coefficients were examined. By non-border binomial coefficient, we mean binomial(n,m) with n >= 4 and 2 >= m >= n-2.
T. D. Noe, Plot of 13 terms
Eric W. Weisstein, MathWorld: Binomial Coefficient
(Mma) nn = 1000000; mx = Binomial[nn, 2]; tb = Table[s = {}; m = 2; While[b = Binomial[n, m]; m <= n/2 && b <= mx, AppendTo[s, b]; m++]; s, {n, nn}]; t2 = Union[Flatten[tb]]; t = Table[0, {15}]; Do[len = Length[FactorInteger[b]]; If[len <= 15 && t[[len]] == 0, t[[len]] = b], {b, t2}]; t
Cf. A048571 (number of prime factors in binomial(n,m)).
nonn,hard
T. D. Noe, Nov 03 2014