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A340810
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Triangle T(n,k), n>=2, 2 <= k <= A214046(n), read by rows, where T(n,k) = n! mod k^n.
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1
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2, 6, 8, 24, 24, 120, 16, 720, 48, 666, 5040, 128, 954, 40320, 384, 8586, 100736, 362880, 768, 26811, 483072, 3628800, 1280, 58725, 2168064, 39916800, 3072, 173259, 9239552, 234860975, 479001600
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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LINKS
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EXAMPLE
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n\k | 2 3 4 5 6
-----+---------------------------------------------
2 | 2;
3 | 6;
4 | 8, 24;
5 | 24, 120;
6 | 16, 720;
7 | 48, 666, 5040;
8 | 128, 954, 40320;
9 | 384, 8586, 100736, 362880;
10 | 768, 26811, 483072, 3628800;
11 | 1280, 58725, 2168064, 39916800;
12 | 3072, 173259, 9239552, 234860975, 479001600;
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MATHEMATICA
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row[n_] := Module[{k = 1, s = {}}, While[k^n <= n!, k++; AppendTo[s, Mod[n!, k^n]]]; s]; Table[row[n], {n, 2, 12}] // Flatten (* Amiram Eldar, Apr 28 2021 *)
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PROG
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(Ruby)
def f(n)
return 1 if n < 2
(1..n).inject(:*)
end
def A(n)
m = f(n)
ary = []
(2..n).each{|i|
j = i ** n
ary << m % j
break if m <= j
}
ary
end
(2..n).map{|i| A(i)}.flatten
end
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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