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

1,2

Comments

Inspired by the 4th row given by Guy.

References

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

Links

Table of n, a(n) for n=1..36.

Example

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;
  ...

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

Crossrefs

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

Sequence in context: A079883 A358041 A066269 * A083785 A046487 A062922

Adjacent sequences: A376554 A376555 A376556 * A376558 A376563 A376564

Keyword

nonn,tabl,new

Author

Stefano Spezia, Sep 28 2024

Status

approved