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A327571 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.

%I A327571 #48 Sep 18 2019 13:43:27
%S A327571 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 A327571 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 A327571 4,4,6,4,4,4,4,6,4,4
%N A327571 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 A327571 Seiichi Manyama, <a href="/A327571/b327571.txt">Rows n = 2..141, flattened</a>
%H A327571 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>.
%F A327571 T(n,1) = T(n,n-1) = A071222(n-2).
%F A327571 T(n,1) <= T(n,k).
%F A327571 T(n,2*m) >= 2 for m >= 1.
%e A327571 n | zeroless polydivisible numbers with all digits the same in base n
%e A327571 --+------------------------------------------------------------------
%e A327571 2 | [1]
%e A327571 3 | [1, 11], [2, 22]
%e A327571 4 | [1], [2, 22, 222], [3]
%e A327571 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 A327571 Triangle begins:
%e A327571 n\k  | 1  2  3  4  5  6  7  8  9 10 11 12
%e A327571 -----+------------------------------------
%e A327571    2 | 1;
%e A327571    3 | 2, 2;
%e A327571    4 | 1, 3, 1;
%e A327571    5 | 2, 2, 4, 2;
%e A327571    6 | 1, 2, 1, 2, 1;
%e A327571    7 | 4, 4, 4, 4, 6, 4;
%e A327571    8 | 1, 2, 1, 2, 1, 3, 1;
%e A327571    9 | 2, 2, 4, 2, 2, 4, 2, 2;
%e A327571   10 | 1, 3, 1, 4, 1, 3, 1, 4, 1;
%e A327571   11 | 2, 2, 6, 2, 2, 6, 2, 2, 6, 2;
%e A327571   12 | 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1;
%e A327571   13 | 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4;
%o A327571 (Ruby)
%o A327571 def T(k, n)
%o A327571   s = 0
%o A327571   (0..n - 2).each{|i|
%o A327571     s += k * n ** i
%o A327571     return i if s % (i + 1) > 0
%o A327571   }
%o A327571   n - 1
%o A327571 end
%o A327571 def A327571(n)
%o A327571   (2..n).map{|i| (1..i - 1).map{|j| T(j, i)}}.flatten
%o A327571 end
%o A327571 p A327571(10)
%Y A327571 Row sums give A327577.
%Y A327571 Cf. A071222, A327545.
%K A327571 nonn,tabl,base
%O A327571 2,2
%A A327571 _Seiichi Manyama_, Sep 17 2019