A271373 -id:A271373 - cp's OEIS frontend

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

Seiichi Manyama, Sep 01 2019

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

			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;

Seiichi Manyama, Rows n = 2..18, flattened
Wikipedia, Polydivisible number.

Row sums give A324020.

Cf. A271373, A327545.

A271374 Total number of polydivisible numbers in base n.

Original entry on oeis.org

3, 16, 38, 128, 324, 1068, 2569, 8381, 20457, 58174, 148059, 441493, 916146, 3722968, 8407790, 23909586, 64576509, 178009925, 466027279, 1409607602, 3507905894, 9694292108, 25391646456, 73838562312, 191793924162, 550333004128

Offset: 2

Martin Renner, Apr 05 2016

			There are a(10) = 20457 polydivisible numbers in base 10, which are listed in A144688.

Wikipedia, Polydivisible number.

Row sums of A271373.

Cf. A109032, A109783, A144688.

a(n) = Sum_{k=1..A109783(n)} A271373(n,k).

a(n) ~ (n-1)*(exp(n)-1)/n.

a(16) from Seiichi Manyama, Sep 01 2019
a(17)-a(18) from Seiichi Manyama, Sep 02 2019
a(19)-a(27) from Max Alekseyev, Sep 08 2021

cp's OEIS Frontend

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.

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