A226382 Largest squarefree triangular number < 10^n.

6, 91, 946, 9870, 99681, 996166, 9992685, 99991011, 999872121, 9999878910, 99999957291, 999999911791, 9999993493045, 99999969965911, 999999863600046, 9999999754307335, 99999999552805215, 999999998765257141, 9999999993293677081, 99999999982591731253, 999999999933106061926

Offset

1,1

Comments

Number of prime factors of a(n): 2, 2, 3, 5, 3, 4, 5, 4, 5, 7, 5, 6, 4, 4, 7, 5, 6, 4, 5, 5, 5, 10, 6, 11, 4, 7, 8, 9, 8, 7. Are a(1) = 6 and a(2) = 91 the only semiprimes?

Links

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

Example

6 = 2*3, 91 = 7*13.

Mathematica

t[n_] := n(n+1)/2; Table[m = 2*10^k // Sqrt // Floor; Select[Table[t[x], {x, m + 1, m - 20, -1}], SquareFreeQ[#] && # < 10^k &, 1][[1]], {k, 30}]
lsftr[i_]:=Module[{g=Floor[(Sqrt[1+8*10^i]-1)/2]}, While[ !SquareFreeQ[ (g(g+1))/2], g--]; (g(g+1))/2]; Join[{6}, Array[lsftr, 20, 2]] (* Harvey P. Dale, Jun 19 2013 *)

Crossrefs

Cf. A005117 (squarefree numbers), A000217 (triangular numbers).

Cf. A061304 (squarefree triangular numbers).

Sequence in context: A305324 A265088 A077370 * A095864 A246155 A349716

Adjacent sequences: A226379 A226380 A226381 * A226383 A226384 A226385

Keyword

nonn

Author

Zak Seidov, Jun 05 2013

Status

approved