A358175 - OEIS

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 #9 Jan 16 2023 09:10:46

%S 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 13,25,241,11,27,30,32,35,33,17,34,36,433,31,39,38,40,42,44,45,48,727,

%U 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 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 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 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 Cf. A001065, A027751, A358082, A064413, A356851, A356430, A354960.

%K nonn

%O 1,2

%A _Scott R. Shannon_, Nov 02 2022