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%I #19 Sep 30 2017 23:59:20
%S 1,2,4,6,3,7,8,10,5,11,12,14,9,15,17,13,18,20,16,22,19,23,24,26,21,27,
%T 29,25,30,32,28,34,31,35,36,38,33,39,41,37,42,44,40,46,43,47,48,50,45,
%U 51,53,49,54,56,52,58,55,59,60,64,57,61,62,66,63,67,68,70,65,71,72,74
%N a(n) = smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) is coprime to n.
%C Sequence is likely to be a permutation of the positive integers, but I am uncertain. A117533(n) = Sum_{k=1..n} a(k). Sequence A117534 is the inverse permutation if this sequence is a permutation of the positive integers.
%H Michael De Vlieger, <a href="/A117532/b117532.txt">Table of n, a(n) for n = 1..3000</a>
%e a(4) = 6 because 6 is the smallest positive integer m not among the first 3 terms of the sequence such that 1+2+4+m is coprime to 4. 1+2+4+3 = 10 and gcd(4,10)=2; 1+2+4+5 = 12 and gcd(4,12)=4; but 1+2+4+6 = 13 and gcd(4,13)=1.
%p A117532 := proc(nmax) local a,n,nxt, asu ; a := [1] ; asu := 1 ; while nops(a) < nmax do n := nops(a)+1 ; nxt := 1 ; while nxt in a or gcd(n, asu+nxt) <> 1 do nxt := nxt+1 ; od ; a := [op(a),nxt] ; asu := asu+nxt ; od ; a ; end: A117532(80) ; # _R. J. Mathar_, May 10 2007
%t Fold[Append[#1, Block[{k = 2}, While[Nand[FreeQ[#1, k], CoprimeQ[Total@ #1 + k, #2]], k++]; k]] &, {1}, Range[2, 72]] (* _Michael De Vlieger_, Sep 30 2017 *)
%Y Cf. A117534, A117533.
%K nonn
%O 1,2
%A _Leroy Quet_, Mar 26 2006
%E More terms from _R. J. Mathar_, May 10 2007