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
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.
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
Comments