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A333432
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A(n,k) is the n-th number m that divides k^m - 1 (or 0 if m does not exist); square array A(n,k), n>=1, k>=1, read by antidiagonals.
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6
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1, 1, 2, 1, 0, 3, 1, 2, 0, 4, 1, 3, 4, 0, 5, 1, 2, 9, 8, 0, 6, 1, 5, 4, 21, 16, 0, 7, 1, 2, 25, 6, 27, 20, 0, 8, 1, 7, 3, 125, 8, 63, 32, 0, 9, 1, 2, 49, 4, 625, 12, 81, 40, 0, 10, 1, 3, 4, 343, 6, 1555, 16, 147, 64, 0, 11, 1, 2, 9, 8, 889, 8, 3125, 18, 171, 80, 0, 12
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 0, 2, 3, 2, 5, 2, 7, 2, ...
3, 0, 4, 9, 4, 25, 3, 49, 4, ...
4, 0, 8, 21, 6, 125, 4, 343, 8, ...
5, 0, 16, 27, 8, 625, 6, 889, 10, ...
6, 0, 20, 63, 12, 1555, 8, 2359, 16, ...
7, 0, 32, 81, 16, 3125, 9, 2401, 20, ...
8, 0, 40, 147, 18, 7775, 12, 6223, 32, ...
9, 0, 64, 171, 24, 15625, 16, 16513, 40, ...
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MAPLE
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A:= proc() local h, p; p:= proc() [1] end;
proc(n, k) if k=2 then `if`(n=1, 1, 0) else
while nops(p(k))<n do for h from 1+p(k)[-1]
while k&^h mod h <> 1 do od;
p(k):= [p(k)[], h]
od; p(k)[n] fi
end
end():
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MATHEMATICA
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A[n_, k_] := Module[{h, p}, p[_] = {1}; If[k == 2, If[n == 1, 1, 0], While[ Length[p[k]] < n, For[h = 1 + p[k][[-1]], Mod[k^h, h] != 1, h++]; p[k] = Append[p[k], h]]; p[k][[n]]]];
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CROSSREFS
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Columns k=1-20 give: A000027, A063524, A067945, A014945, A067946, A014946, A067947, A014949, A068382, A014950, A068383, A014951, A116621, A177805, A014957, A177807, A128358, A333506, A128360.
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KEYWORD
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AUTHOR
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STATUS
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approved
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