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%I #8 Nov 29 2022 01:34:42
%S 1,2,9,7,24,24,56,34,151,62,173,187,264,151,530,218,679,528,737,405,
%T 1558,638,1256,1002,1871,852,3567,1053,2472,2109,2908,2226,5433,1840,
%U 4113,3523,6356,2537,9598,2944,7311,6424,7429,3883,13592,5058,11576,7982,12123,5638,17971,8613,16766,11201
%N Number of orbits of the group of units of Z/(n) acting naturally on the 4-subsets of Z/(n).
%e a(5) = 2 since when U(5) = {1,2,3,4} acts naturally on the five 4-subsets {0,1,2,3}, {0,1,2,4}, {0,1,3,4}, {0,2,3,4}, {1,2,3,4} of Z/(5) the orbits are {{0,1,2,3},{0,1,2,4}, {0,1,3,4}, {0,2,3,4}} and {{1,2,3,4}}.
%p g:= proc(n) local U, S, C, R,u,s,Cr,us,v;
%p U:= select(t -> igcd(n,t)=1, [$1..n-1]);
%p S:= combinat:-choose({$0..n-1},4);
%p C:= S;
%p for s in S do R[s]:= s od;
%p for u in U do
%p Cr:= NULL;
%p for s in C do
%p us:= map(t -> u*t mod n, s);
%p v:= R[us];
%p while R[v] <> v do v:= R[v] od;
%p if v <> s then R[s]:= v; Cr:= Cr, s fi
%p od;
%p C:= C minus {Cr};
%p od;
%p nops(C)
%p end proc;
%p map(g, [$4..60]); # _Robert Israel_, Nov 28 2022
%Y Cf. A063379, A065957, A000005, A056376 + 1, A056371 - 1
%K nonn
%O 4,2
%A _W. Edwin Clark_, Jul 15 2001
%E Offset corrected, and more terms by _Robert Israel_, Nov 28 2022
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