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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. 2
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, 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, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Seiichi Manyama, Rows n = 2..141, flattened

Wikipedia, Polydivisible number.

FORMULA

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

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

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

EXAMPLE

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

--+------------------------------------------------------------------

2 | [1]

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

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

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.

Triangle begins:

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

-----+------------------------------------

   2 | 1;

   3 | 2, 2;

   4 | 1, 3, 1;

   5 | 2, 2, 4, 2;

   6 | 1, 2, 1, 2, 1;

   7 | 4, 4, 4, 4, 6, 4;

   8 | 1, 2, 1, 2, 1, 3, 1;

   9 | 2, 2, 4, 2, 2, 4, 2, 2;

  10 | 1, 3, 1, 4, 1, 3, 1, 4, 1;

  11 | 2, 2, 6, 2, 2, 6, 2, 2, 6, 2;

  12 | 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1;

  13 | 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4;

PROG

(Ruby)

def T(k, n)

  s = 0

  (0..n - 2).each{|i|

    s += k * n ** i

    return i if s % (i + 1) > 0

  }

  n - 1

end

def A327571(n)

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

end

p A327571(10)

CROSSREFS

Row sums give A327577.

Cf. A071222, A327545.

Sequence in context: A320040 A072528 A227083 * A166363 A117470 A070786

Adjacent sequences:  A327568 A327569 A327570 * A327572 A327573 A327574

KEYWORD

nonn,tabl,base

AUTHOR

Seiichi Manyama, Sep 17 2019

STATUS

approved

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Last modified January 20 23:29 EST 2020. Contains 331104 sequences. (Running on oeis4.)