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%I #9 May 12 2018 12:54:41
%S 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,3,
%T 4,4,1,3,4,4,1,3,4,4,1,3,4,4,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,5,2,
%U 3,5,1,3,5,2,3,5,1,3,5,2,1,3,3,3,7,7,3,3,7,7,3,3,7,7,3,3,1,3,1,3,1,0,4,3,1
%N Irregular array a(m,k) = A001035(k) mod m read by rows, 1<=k<=16, 3<=m.
%C Conjectures (based on mod values up to n=99): the sequence A001035(m) is (pre)periodic modulo n for all n, the lengths of the ending periods mod n (except n=4) being given by A011773 (which is related to Carmichael's lambda function).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelFunction.html">Carmichael Function</a>
%e The array starts in row m=3 as:
%e 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0;
%e 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3;
%e 1 3 4 4 1 3 4 4 1 3 4 4 1 3 4 4;
%e 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3;
%e 1 3 5 2 3 5 1 3 5 2 3 5 1 3 5 2;
%e 1 3 3 3 7 7 3 3 7 7 3 3 7 7 3 3;
%e 1 3 1 3 1 0 4 3 1 3 1 0 4 3 1 3;
%e 1 3 9 9 1 3 9 9 1 3 9 9 1 3 9 9;
%e 1 3 8 10 7 3 10 10 1 6 1 3 8 10 7 3;
%e 1 3 7 3 7 3 7 3 7 3 7 3 7 3 7 3;
%t seq = List[1, 3, 19, 219, 4231, 130023, 6129859, 431723379, 44511042511, 6611065248783, 1396281677105899, 414864951055853499, 171850728381587059351, 98484324257128207032183, 77567171020440688353049939, 83480529785490157813844256579] Table[Mod[seq, i], {i, 3, 9}]
%Y Cf. A001035, A011773, A002322.
%K nonn,tabf
%O 3,18
%A _Gerald McGarvey_, Feb 26 2005
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