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A324020 Total number of zeroless polydivisible numbers in base n.

%I A324020 #32 Sep 14 2019 22:32:10
%S A324020 1,4,9,32,45,236,330,1108,2157,12740,7713,93710,65602,230342,570128,
%T A324020 5007682,2484863,36896861,16618196,81481351,266303823,1991227852,
%U A324020 533069755,7599786619,13636829615,35633175288,43994413188,796513902354,121485971111,5858898939564
%N A324020 Total number of zeroless polydivisible numbers in base n.
%H A324020 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>.
%F A324020 a(n) = Sum_{k=1..n-1} A324019(n,k).
%e A324020 n | polydivisible numbers in base n  | zeroless
%e A324020 --+----------------------------------+---------------
%e A324020 2 | [0, 1]                           | [1]
%e A324020   | [10]                             |
%e A324020 --+----------------------------------+---------------
%e A324020 3 | [0, 1, 2]                        | [1, 2]
%e A324020   | [11, 20, 22]                     | [11, 22]
%e A324020   | [110, 200, 220]                  |
%e A324020   | [1100, 2002, 2200]               |
%e A324020   | [11002, 20022]                   |
%e A324020   | [110020, 200220]                 |
%e A324020 --+----------------------------------+----------------
%e A324020 4 | [0, 1, 2, 3]                     | [1, 2, 3]
%e A324020   | [10, 12, 20, 22, 30, 32]         | [12, 22, 32]
%e A324020   | [102, 120, 123, 201,             | [123, 222, 321]
%e A324020   |  222, 300, 303, 321]             |
%e A324020   | [1020, 1200, 1230, 2010,         |
%e A324020   |  2220, 3000, 3030, 3210]         |
%e A324020   | [10202, 12001, 12303, 20102,     |
%e A324020   |  22203, 30002, 32103]            |
%e A324020   | [120012, 123030, 222030, 321030] |
%e A324020   | [2220301]                        |
%o A324020 (Ruby)
%o A324020 def A(n)
%o A324020   d = 0
%o A324020   a = (1..n - 1).map{|i| [i]}
%o A324020   cnt = n - 1
%o A324020   while d < n - 2
%o A324020     d += 1
%o A324020     b = []
%o A324020     a.each{|i|
%o A324020       (1..n - 1).each{|j|
%o A324020         m = i.clone + [j]
%o A324020         if (0..d).inject(0){|s, k| s + m[k] * n ** (d - k)} % (d + 1) == 0
%o A324020           b << m
%o A324020           cnt += 1
%o A324020         end
%o A324020       }
%o A324020     }
%o A324020     a = b
%o A324020   end
%o A324020   cnt
%o A324020 end
%o A324020 def A324020(n)
%o A324020   (2..n).map{|i| A(i)}
%o A324020 end
%o A324020 p A324020(10)
%Y A324020 Cf. A181736, A271374, A324019, A324205.
%K A324020 nonn,base
%O A324020 2,2
%A A324020 _Seiichi Manyama_, Sep 01 2019
%E A324020 a(20)-a(31) from _Bert Dobbelaere_, Sep 14 2019