A358201 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with sigma(max_{k=1..n-1}a(k)).

1, 2, 3, 4, 7, 6, 8, 5, 9, 13, 10, 12, 14, 15, 16, 31, 18, 20, 22, 24, 26, 28, 30, 32, 21, 27, 33, 34, 36, 35, 39, 38, 40, 25, 42, 44, 45, 46, 48, 50, 51, 52, 49, 54, 55, 56, 57, 58, 60, 62, 63, 64, 127, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108

Offset: 1

Author

Scott R. Shannon, Nov 03 2022

Keywords

• nonn
• look

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 150000 terms the fixed points are 1, 2, 3, 4, 6, 9, 12, 93, 6003, 6881, 16269, 100707, 114839, 116999. It is likely more exist.

Examples

			a(9) = 9 as sigma(max_{k=1..8}a(k)) = sigma(8) = A000203(8) = 15, and 9 is the smallest unused number that shares a factor with 15.
		

Links

• Scott R. Shannon, Image of the first 150000 terms. The green line is a(n) = n.

Crossrefs

Cf. A000203, A358176, A358082, A064413, A356851, A356430, A354960.