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%I #19 Dec 29 2023 10:58:54
%S 3,6,9,18,12,16,8,24,32,34,30,48,15,1,14,2,17,11,20,4,26,7,21,22,5,27,
%T 10,13,25,40,19,28,33,37,23,42,38,44,35,31,41,29,46,49,39,50,36,43,47,
%U 45,51,54,55,53,52,56,57,62,61,60,64,68,67,58,63,70,69,71,65,77,66,72
%N a(1)=3. a(n) is the smallest positive integer not occurring earlier in the sequence such that (sum{k=1 to n} a(k)) divides product{j=1 to n} a(j).
%C Is this a permutation of the positive integers? According to Hans Havermann, this sequence matches sequence A127562 beginning with the 104th term of each. Unlike sequence A127562, the sum of the first n terms of this sequence divides the product of the first n terms for every positive integer n.
%p N:= 1000: # to get a(1) to a(m-1) where a(m) is the first term > N
%p a[1]:= 3:
%p R:= {$1..N} minus {3}:
%p P:= 3:
%p S:= 3:
%p success:= true:
%p for n from 2 while success and R <> {} do
%p success := false;
%p for r in R do
%p if type((P*r)/(S+r),integer) then
%p a[n]:= r;
%p nmax:= n;
%p R:= R minus {r};
%p success:= true;
%p P:= P * r;
%p S:= S + r;
%p break
%p fi
%p od:
%p od:
%p seq(a[i],i=1..nmax); # _Robert Israel_, Dec 13 2014
%t f[l_List] := Block[{k = 1, s = Plus @@ l, p = Times @@ l},While[MemberQ[l, k] || Mod[k*p, k + s] > 0, k++ ];Append[l, k]];Nest[f, {3}, 75] (* _Ray Chandler_, Jan 22 2007 *)
%o (PARI) v=[3];print1(3,", ");n=1;while(n<100,p=prod(i=1,#v,v[i]);if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);print1(n,", ");n=0);n++) \\ _Derek Orr_, Dec 13 2014
%Y Cf. A127562, A127645, A127646.
%K nonn
%O 1,1
%A _Leroy Quet_, Jan 22 2007
%E Extended by _Ray Chandler_, Jan 22 2007
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