cp's OEIS Frontend

A127562 a(1)=1. a(2)=2. For n>=3, a(n) is the smallest positive integer not occurring earlier in the sequence such that (Sum_{k=1..n} a(k)) divides Product_{j=1..n} a(j).

%I A127562 #19 Dec 29 2023 10:59:16
%S A127562 1,2,3,6,4,8,12,18,10,16,20,25,19,27,9,36,24,30,15,35,22,33,5,38,14,
%T A127562 43,11,26,13,7,28,34,31,21,17,23,29,39,44,42,40,32,45,51,37,47,48,50,
%U A127562 52,46,56,60,41,55,54,58,53,57,49,62,59,61,63,64,65,69,66,70,68,73,71,77,67
%N A127562 a(1)=1. a(2)=2. For n>=3, a(n) is the smallest positive integer not occurring earlier in the sequence such that (Sum_{k=1..n} a(k)) divides Product_{j=1..n} a(j).
%C A127562 Is this a permutation of the positive integers?
%H A127562 Ivan Neretin, <a href="/A127562/b127562.txt">Table of n, a(n) for n = 1..1000</a>
%e A127562 a(1)+a(2)+a(3)+a(4)+a(5)+a(6) = 1+2+3+6+4+8 = 24. a(1)*a(2)*a(3)*a(4)*a(5)*a(6) = 1152. And 24 divides 1152. Had a(6) been any of the positive integers which are < 8 and do not occur earlier in the sequence (i.e., had it been 5 or 7), then the sum of the first 6 terms of the sequence would not have divided the product of the first 6 terms.
%t A127562 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, {1, 2}, 75] (* _Ray Chandler_, Jan 22 2007 *)
%Y A127562 Cf. A127563, A127564.
%K A127562 nonn
%O A127562 1,2
%A A127562 _Leroy Quet_, Jan 18 2007
%E A127562 Extended by _Ray Chandler_, Jan 22 2007