A238336 The first row of Pascal's triangle having exactly n distinct squarefree numbers, or -1 if no such row exists.

0, 2, 5, 7, 13, 11, 15, 44, 53, 46, 59, 23, 43, 278, 191, 143, 79, 119, 187, 62, 47, 221, 214, 1643, 159, 238, 95, 473, 314, 3583, 671, 474, 958, 3071, 5719, 215, 1439, 7423, 1663, 447, 223, 3695, 4346, 4318, 12983, 319, 35069, 5983, 5471, 8567, 959, 3067

Offset: 1

Author

T. D. Noe, Mar 05 2014

Keywords

• nonn
• more
• hard

Links

• A. Granville and O. Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107, [DOI].

Crossrefs

Cf. A064461, A238337.

Programs

Mathematica

nn = 20; t = Table[-1, {nn}]; found = 0; n = -1; While[found < nn, n++; len = Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]]; If[0 < len <= nn && t[[len]] == -1, t[[len]] = n; found++]]; t

Extensions

Extended by T. D. Noe, Mar 07 2014