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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).

%I A271373 #30 Sep 11 2021 10:10:40
%S A271373 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,
%T A271373 54,54,49,46,21,3,1,7,21,49,87,121,145,145,145,121,92,56,33,20,14,7,3,
%U A271373 1,1,8,28,74,148,238,324,367,367,320,258,188,122,69,37,12,6,3
%N 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).
%H A271373 Max Alekseyev, <a href="/A271373/b271373.txt">Table of n, a(n) for n = 2..810</a>
%H A271373 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>.
%F A271373 T(n,k) ~ (n-1)*n^(k-1)/k!
%F A271373 T(10,k) = A143671(k), 1 <= k <= 25.
%e A271373 The triangle begins
%e A271373 n\k 1  2  3  4  5  6  7  8  9 10 ...
%e A271373 2:  2  1
%e A271373 3:  3  3  3  3  2  2
%e A271373 4:  4  6  8  8  7  4  1
%e A271373 5:  5 10 17 21 21 21 13 10  6  4
%e A271373 ...
%p A271373 b:=10; # Base
%p A271373 P:={seq(i,i=1..b-1)}: # Polydivisible numbers
%p A271373 M:=[nops(P)+1]: # Number of k-digit polydivisible numbers
%p A271373 for i from 2 while nops(P)>0 do
%p A271373   Q:={}:
%p A271373   for n from 1 to nops(P) do
%p A271373     for j from 0 to b-1 do
%p A271373       if P[n]*b+j mod i = 0 then Q:={op(Q),P[n]*b+j}: fi:
%p A271373     od:
%p A271373   od:
%p A271373   M:=[op(M),nops(Q)]:
%p A271373   P:=Q;
%p A271373 od:
%p A271373 T||b:=op(M[1..nops(M)-1]); # Table row T(n,k) for n = b
%Y A271373 Cf. A109783 (row lengths), A143671 (row n=10), A144688, A271374 (row sums).
%K A271373 nonn,base,tabf
%O A271373 2,1
%A A271373 _Martin Renner_, Apr 05 2016
%E A271373 Rows n=17 to n=25 added to b-file by _Max Alekseyev_, Sep 11 2021