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A124823 a(n) = n-th integer from among those positive integers which are coprime to n(n+1)/2.

%I A124823 #15 Mar 29 2018 04:27:44
%S A124823 1,2,7,9,8,10,15,23,16,13,35,37,16,31,53,33,26,28,49,83,40,25,71,89,
%T A124823 33,41,95,67,56,58,63,103,58,53,151,109,40,64,157,101,73,74,95,179,88,
%U A124823 49,143,167,71,98,175,113,80,109,173,199,92,61,223,227,64,110,221,173,142
%N A124823 a(n) = n-th integer from among those positive integers which are coprime to n(n+1)/2.
%H A124823 Robert Israel, <a href="/A124823/b124823.txt">Table of n, a(n) for n = 1..10000</a>
%e A124823 The positive integers which are coprime to (5*6/2)=15 are 1,2,4,7,8,11,13,14... The fifth of these integers is 8, so a(5) = 8.
%p A124823 f:= proc(n) local t,k, count;
%p A124823     t:= n*(n+1)/2; count:= 0;
%p A124823     for k from 1 do
%p A124823       if igcd(k,t)=1 then count:= count+1; if count = n then return k fi fi
%p A124823     od
%p A124823 end proc:
%p A124823 map(f, [$1..100]); # _Robert Israel_, Mar 29 2018
%t A124823 f[n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[n*(n + 1)/2, k] > 1, k++ ];c--;];k];Table[f[n], {n, 65}] (* _Ray Chandler_, Nov 10 2006 *)
%Y A124823 Cf. A124822.
%K A124823 nonn,look
%O A124823 1,2
%A A124823 _Leroy Quet_, Nov 08 2006
%E A124823 Extended by _Ray Chandler_, Nov 10 2006