A376557 Triangle read by rows: the n-th row gives the least sequence of n consecutive numbers with the same number of divisors.

1, 2, 3, 33, 34, 35, 242, 243, 244, 245, 11605, 11606, 11607, 11608, 11609, 28374, 28375, 28376, 28377, 28378, 28379, 171893, 171894, 171895, 171896, 171897, 171898, 171899, 1043710445721, 1043710445722, 1043710445723, 1043710445724, 1043710445725, 1043710445726, 1043710445727, 1043710445728

Offset: 1

Author

Stefano Spezia, Sep 28 2024

Keywords

• nonn
• tabl

Comments

Inspired by the 4th row given by Guy.

Examples

			The triangle begins as:
       1;
       2,      3;
      33,     34,     35;
     242,    243,    244,    245;
   11605,  11606,  11607,  11608,  11609;
   28374,  28375,  28376,  28377,  28378,  28379;
  171893, 171894, 171895, 171896, 171897, 171898, 171899;
  ...
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B18.

Crossrefs

Cf. A000005, A006558 (1st column), A019273 (right diagonal), A039665.

Programs

Mathematica

row[n_]:=Module[{}, k=1; nd=DivisorSigma[0,k]; While[Product[Boole[DivisorSigma[0,k+i]==nd], {i, n-1}]!=1, k++; nd=DivisorSigma[0,k]]; Table[i+k, {i, 0, n-1}]]; Array[row, 7]//Flatten