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%I #27 Jun 16 2021 15:33:59
%S 4,12,8,24,6,10,16,20,25,3,7,5,22,13,1,19,14,11,27,9,17,2,29,15,21,23,
%T 28,34,30,31,18,35,33,26,32,37,36,38,39,45,42,43,40,49,41,48,46,44,47,
%U 50,51,54,55,53,52,56,57,62,61,60,64,68,67,58,63,70,69,71,65,77,66,72,74,73,59
%N a(0)=4. a(n) is the smallest number not in the sequence such that Sum_{k=1..n} a(k) divides Product_{k=1..n} a(k).
%C Conjectured to be a permutation of the natural numbers.
%t f[lst_List] := Block[{k = 1, s = Plus @@ lst, p = Times @@ lst}, While[ MemberQ[lst, k] || Mod[p*k, s + k] > 0, k++]; Append[ lst, k]]; Nest[f, {3}, 75] (* _Robert G. Wilson v_, Jan 19 2015 *)
%o (PARI) v=[4]; print1(4,", ");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++)
%Y Cf. A127644.
%K nonn
%O 0,1
%A _Derek Orr_, Jan 17 2015
%E Offset corrected by _N. J. A. Sloane_, Jun 16 2021
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