cp's OEIS Frontend

A358175 a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m.

%I A358175 #9 Jan 16 2023 09:10:46
%S A358175 1,2,3,4,5,6,8,19,10,7,29,9,12,14,15,18,16,20,127,22,24,26,28,21,233,
%T A358175 13,25,241,11,27,30,32,35,33,17,34,36,433,31,39,38,40,42,44,45,48,727,
%U A358175 46,50,797,49,52,51,54,57,37,60,56,55,58,62,63,1259,64,66,69,68,70,65,1579,72,78,77,74
%N A358175 a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m.
%C A358175 The sequence is conjectured to be a permutation of the positive integers. In the first 10000 terms, other than the first three terms, there are thirty-five fixed points, the last being 2051. It is plausible no more exist although this is unknown.
%e A358175 a(9) = 10 as Sum_{k=1..8} A001065(a(k)) = 0 + 1 + 1 + 3 + 1 + 6 + 7 + 1 = 20, and 10 is the smallest unused number that shares a factor with 20.
%Y A358175 Cf. A001065, A027751, A358082, A064413, A356851, A356430, A354960.
%K A358175 nonn
%O A358175 1,2
%A A358175 _Scott R. Shannon_, Nov 02 2022