A327571 - OEIS

%I #48 Sep 18 2019 13:43:27

%S 1,2,2,1,3,1,2,2,4,2,1,2,1,2,1,4,4,4,4,6,4,1,2,1,2,1,3,1,2,2,4,2,2,4,

%T 2,2,1,3,1,4,1,3,1,4,1,2,2,6,2,2,6,2,2,6,2,1,2,1,2,1,3,1,2,1,2,1,4,4,

%U 4,4,6,4,4,4,4,6,4,4

%N Triangle T(n,k) read by rows giving the number of zeroless polydivisible numbers in base n that contains only "k" in the digits with 1 <= k <= n-1.

%H Seiichi Manyama, <a href="/A327571/b327571.txt">Rows n = 2..141, flattened</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>.

%F T(n,1) = T(n,n-1) = A071222(n-2).

%F T(n,1) <= T(n,k).

%F T(n,2*m) >= 2 for m >= 1.

%e n | zeroless polydivisible numbers with all digits the same in base n

%e --+------------------------------------------------------------------

%e 2 | [1]

%e 3 | [1, 11], [2, 22]

%e 4 | [1], [2, 22, 222], [3]

%e So T(2,1) = 1, T(3,1) = 2, T(3,2) = 2, T(4,1) = 1, T(4,2) = 3, T(4,3) = 1.

%e Triangle begins:

%e n\k  | 1  2  3  4  5  6  7  8  9 10 11 12

%e -----+------------------------------------

%e    2 | 1;

%e    3 | 2, 2;

%e    4 | 1, 3, 1;

%e    5 | 2, 2, 4, 2;

%e    6 | 1, 2, 1, 2, 1;

%e    7 | 4, 4, 4, 4, 6, 4;

%e    8 | 1, 2, 1, 2, 1, 3, 1;

%e    9 | 2, 2, 4, 2, 2, 4, 2, 2;

%e   10 | 1, 3, 1, 4, 1, 3, 1, 4, 1;

%e   11 | 2, 2, 6, 2, 2, 6, 2, 2, 6, 2;

%e   12 | 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1;

%e   13 | 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4;

%o (Ruby)

%o def T(k, n)

%o   s = 0

%o   (0..n - 2).each{|i|

%o     s += k * n ** i

%o     return i if s % (i + 1) > 0

%o   }

%o   n - 1

%o end

%o def A327571(n)

%o   (2..n).map{|i| (1..i - 1).map{|j| T(j, i)}}.flatten

%o end

%o p A327571(10)

%Y Row sums give A327577.

%Y Cf. A071222, A327545.

%K nonn,tabl,base

%O 2,2

%A _Seiichi Manyama_, Sep 17 2019