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A271773 a(1) = 0, then a(n) is the maximum of all 0 < m < n for which n == a(m) (mod m).

%I A271773 #11 Apr 15 2016 19:01:03
%S A271773 0,1,2,1,4,1,6,3,5,1,10,1,12,9,2,1,16,1,18,7,11,1,22,5,13,3,20,1,28,1,
%T A271773 30,21,17,7,8,1,36,25,5,1,40,1,42,39,23,1,46,7,16,33,14,1,52,11,48,19,
%U A271773 29,1,58,1,60,15,38,13,54,1,66,45,7,1,70,1,72,27
%N A271773 a(1) = 0, then a(n) is the maximum of all 0 < m < n for which n == a(m) (mod m).
%H A271773 Peter Kagey, <a href="/A271773/b271773.txt">Table of n, a(n) for n = 1..10000</a>
%e A271773 a(1) = 0 by definition.
%e A271773 a(2) = 1 because a(1) == 2 (mod 1).
%e A271773 a(3) = 2 because a(2) == 3 (mod 2).
%e A271773 a(4) = 1 because a(1) == 4 (mod 1).
%e A271773 a(5) = 4 because a(4) == 5 (mod 4).
%e A271773 a(6) = 1 because a(1) == 6 (mod 1).
%e A271773 a(7) = 6 because a(6) == 7 (mod 6).
%e A271773 a(8) = 3 because a(3) == 8 (mod 3).
%t A271773 a[1] = 0; a[n_] := a[n] = Max@ Select[Range[n - 1], Mod[n, #] == Mod[a[#], #] &]; Table[a@ n, {n, 75}] (* _Michael De Vlieger_, Apr 15 2016 *)
%Y A271773 Cf. A269423, A269427, A271530, A271531, A271774.
%K A271773 nonn
%O A271773 1,3
%A A271773 _Peter Kagey_, Apr 14 2016