A271373 Triangle T(n,k) read by rows giving the number of k-digit polydivisible numbers (see A144688) in base n with 1 <= k <= A109783(n).

2, 1, 3, 3, 3, 3, 2, 2, 4, 6, 8, 8, 7, 4, 1, 5, 10, 17, 21, 21, 21, 13, 10, 6, 4, 6, 15, 30, 45, 54, 54, 49, 46, 21, 3, 1, 7, 21, 49, 87, 121, 145, 145, 145, 121, 92, 56, 33, 20, 14, 7, 3, 1, 1, 8, 28, 74, 148, 238, 324, 367, 367, 320, 258, 188, 122, 69, 37, 12, 6, 3

Offset: 2

Author

Martin Renner, Apr 05 2016

Keywords

• nonn
• base
• tabf

Examples

			The triangle begins
n\k 1  2  3  4  5  6  7  8  9 10 ...
2:  2  1
3:  3  3  3  3  2  2
4:  4  6  8  8  7  4  1
5:  5 10 17 21 21 21 13 10  6  4
...
		

Links

• Max Alekseyev, Table of n, a(n) for n = 2..810
• Wikipedia, Polydivisible number.

Crossrefs

Cf. A109783 (row lengths), A143671 (row n=10), A144688, A271374 (row sums).

Programs

Maple

b:=10; # Base
P:={seq(i,i=1..b-1)}: # Polydivisible numbers
M:=[nops(P)+1]: # Number of k-digit polydivisible numbers
for i from 2 while nops(P)>0 do
  Q:={}:
  for n from 1 to nops(P) do
    for j from 0 to b-1 do
      if P[n]*b+j mod i = 0 then Q:={op(Q),P[n]*b+j}: fi:
    od:
  od:
  M:=[op(M),nops(Q)]:
  P:=Q;
od:
T||b:=op(M[1..nops(M)-1]); # Table row T(n,k) for n = b

Formula

T(n,k) ~ (n-1)*n^(k-1)/k!

T(10,k) = A143671(k), 1 <= k <= 25.

Extensions

Rows n=17 to n=25 added to b-file by Max Alekseyev, Sep 11 2021