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%I #14 Mar 29 2016 23:36:28
%S 0,0,0,0,0,4,0,6,6,4,0,8,0,4,6,6,0,4,0,6,6,4,0,9,10,4,6,6,0,4,0,6,6,4,
%T 10,8,0,4,6,6,0,4,0,6,6,4,0,9,14,4,6,6,0,4,10,6,6,4,0,8,0,4,6,6,10,4,
%U 0,6,6,4,0,10,0,4,6,6,14,4,0,6,6,4,0,8,10,4,6,6,0,4,14,6,6,4,10,9,0,4,6
%N Smallest number that is neither a divisor of nor relatively prime to n, or 0 if no such number exists.
%C Original name: Smallest number of "unrelated set" belonging to n [=URS(n)]. Least number, neither divisor nor relatively prime to n. Or a(n)=0 if unrelated set is empty.
%C From _Michael De Vlieger_, Mar 28 2016 (Start):
%C Primes n have no unrelated numbers m < n since all such numbers are coprime to n.
%C Unrelated numbers m must be composite since primes must either divide or be coprime to n.
%C m = 1 is not counted as unrelated as it divides and is coprime to n.
%C a(4) = 0 since 4 is the smallest composite and unrelated numbers m with respect to n must be composite and smaller than n. All other composite n have at least one unrelated number m.
%C The test for unrelated numbers m that belong to n is 1 < gcd(m, n) < m.
%C a(6) = A073759(6), a(8) = A073759(8), a(9) = A073759(9).
%C (End)
%H Michael De Vlieger, <a href="/A073758/b073758.txt">Table of n, a(n) for n = 1..10000</a>
%e a(20) = 6 since it is the smallest term of the set of numbers m that neither divide nor are coprime to 20, i.e., {6, 8, 12, 14, 15, 16, 18}.
%t tn[x_] := Table[w, {w, 1, x}]; di[x_] := Divisors[x]; dr[x_] := Union[di[x], rrs[x]]; rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]]; unr[x_] := Complement[tn[x], dr[x]]; Table[Min[unr[w]], {w, 1, 128}]. (* + or -Infinity is replaced by 0 *)
%t Table[SelectFirst[Range[4, n - 2], 1 < GCD[#, n] < # &] /. n_ /; MissingQ@ n -> 0, {n, 99}] (* _Michael De Vlieger_, Mar 28 2016, Version 10.2 *)
%o (PARI) a(n) = {for(k=1, n-1, if ((gcd(n,k) != 1) && (n % k), return (k));); 0;} \\ _Michel Marcus_, Mar 29 2016
%Y Cf. A045763.
%K nonn
%O 1,6
%A _Labos Elemer_, Aug 08 2002
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