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A062169 Triangle T(n, k) = k! mod n for n >= 1, 1 <= k <= n.

%I A062169 #17 Oct 27 2021 15:01:29
%S A062169 0,1,0,1,2,0,1,2,2,0,1,2,1,4,0,1,2,0,0,0,0,1,2,6,3,1,6,0,1,2,6,0,0,0,
%T A062169 0,0,1,2,6,6,3,0,0,0,0,1,2,6,4,0,0,0,0,0,0,1,2,6,2,10,5,2,5,1,10,0,1,
%U A062169 2,6,0,0,0,0,0,0,0,0,0,1,2,6,11,3,5,9,7,11,6,1,12,0,1,2,6,10,8,6,0,0,0,0,0
%N A062169 Triangle T(n, k) = k! mod n for n >= 1, 1 <= k <= n.
%H A062169 Harry J. Smith, <a href="/A062169/b062169.txt">Table of n, a(n) for n=1..1275</a>
%e A062169 a(7,4) = 4! mod 7 = 24 mod 7 = 3. Rows are:
%e A062169 0;
%e A062169 1,0;
%e A062169 1,2,0;
%e A062169 1,2,2,0;
%e A062169 1,2,1,4,0;
%e A062169 1,2,0,0,0,0;
%e A062169 1,2,6,3,1,6,0;
%e A062169 1,2,6,0,0,0,0,0;
%e A062169 1,2,6,6,3,0,0,0,0;
%e A062169 1,2,6,4,0,0,0,0,0,0;
%t A062169 Table[Mod[Range[n]!, n], {n, 1, 15}] // Flatten (* _Jean-François Alcover_, Oct 25 2013 *)
%o A062169 (PARI) { n=0; for (k=1, 50, for (m=1, k, write("b062169.txt", n++, " ", m!%k)) ) } \\ _Harry J. Smith_, Aug 02 2009
%Y A062169 First zero in each row is when k=A002034. Maximum value in each row is A062170. Number of distinct values in each row is A038203. Cf. A000142, A048158, A051127.
%K A062169 nonn,tabl
%O A062169 1,5
%A A062169 _Henry Bottomley_, Jun 11 2001
%E A062169 Definition amended by _Georg Fischer_, Oct 27 2021