A324019 Triangle T(n,k) read by rows giving the number of k-digit zeroless polydivisible numbers in base n with 1 <= k <= n-1.

1, 2, 2, 3, 3, 3, 4, 8, 10, 10, 5, 10, 10, 10, 10, 6, 18, 36, 52, 62, 62, 7, 21, 49, 49, 68, 68, 68, 8, 32, 64, 128, 205, 205, 233, 233, 9, 36, 108, 216, 216, 324, 416, 416, 416, 10, 50, 166, 416, 832, 1382, 1967, 2465, 2726, 2726, 11, 55, 165, 330, 726, 726, 1140, 1140, 1140, 1140, 1140

Offset

2,2

Comments

For k >= n there is no k-digit zeroless polydivisible number in base n.

Links

Seiichi Manyama, Rows n = 2..18, flattened

Wikipedia, Polydivisible number.

Example

Triangle begins:
n\k  | 1   2    3    4    5    6    7    8    9
-----+------------------------------------------
   2 | 1;
   3 | 2,  2;
   4 | 3,  3,   3;
   5 | 4,  8,  10,  10;
   6 | 5, 10,  10,  10,  10;
   7 | 6, 18,  36,  52,  62,  62;
   8 | 7, 21,  49,  49,  68,  68,  68;
   9 | 8, 32,  64, 128, 205, 205, 233, 233;
  10 | 9, 36, 108, 216, 216, 324, 416, 416, 416;

Crossrefs

Row sums give A324020.

Cf. A271373, A327545.

Sequence in context: A110868 A110869 A110876 * A275378 A300506 A300888

Adjacent sequences: A324016 A324017 A324018 * A324020 A324021 A324022

Keyword

nonn,tabl,base

Author

Seiichi Manyama, Sep 01 2019

Status

approved