A358082 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} sigma(a(k)).

1, 2, 4, 11, 23, 47, 5, 101, 7, 211, 3, 14, 22, 487, 6, 9, 8, 10, 1033, 12, 15, 13, 18, 16, 2203, 21, 46, 26, 29, 4583, 89, 9257, 20, 28, 35, 18661, 24, 17, 27, 37441, 30, 19, 25, 32, 33, 36, 34, 38, 39, 40, 42, 44, 45, 48, 37, 31, 50, 49, 52, 54, 56, 58, 60, 62, 63, 51, 57, 64, 55, 66, 69, 72

Offset: 1

Author

Scott R. Shannon, Nov 02 2022

Keywords

• nonn

Comments

The sequence shows large jumps in value due to the sum occasionally forming a large prime, e.g., a(279) = 2650277753. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(7) = 5 as Sum_{k=1..6} sigma(a(k)) = Sum_{k=1..6} A000203(a(k)) = 1 + 3 + 7 + 12 + 24 + 48 = 95, and 5 is the smallest unused number that shares a factor with 95.
		

Crossrefs

Cf. A000203, A358176, A358201, A064413, A356851, A356430, A354960.