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.

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

Offset: 1

Author

Scott R. Shannon, Nov 02 2022

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

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