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A340810
Triangle T(n,k), n>=2, 2 <= k <= A214046(n), read by rows, where T(n,k) = n! mod k^n.
1
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
OFFSET
2,1
LINKS
EXAMPLE
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;
MATHEMATICA
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 *)
PROG
(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
def A340810(n)
(2..n).map{|i| A(i)}.flatten
end
p A340810(12)
CROSSREFS
Column k=2..4 give A068496, A212309, A212310.
Sequence in context: A240644 A344914 A068496 * A334898 A081957 A334901
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, Jan 22 2021
STATUS
approved