A356430 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with the number of divisors of a(n-1).

1, 2, 4, 3, 6, 8, 10, 12, 9, 15, 14, 16, 5, 18, 20, 21, 22, 24, 26, 28, 27, 30, 32, 33, 34, 36, 39, 38, 40, 42, 44, 45, 46, 48, 25, 51, 50, 52, 54, 56, 58, 60, 57, 62, 64, 7, 66, 68, 63, 69, 70, 72, 74, 76, 75, 78, 80, 35, 82, 84, 81, 55, 86, 88, 90, 87, 92, 93, 94, 96, 98, 99, 100, 102, 104

Offset: 1

Author

Scott R. Shannon, Aug 07 2022

Keywords

• nonn

Comments

The sequence is conjectured to be a permutation of the positive integers although it may take a large number of terms for the primes to appear, e.g., 19 has not occurred after 100000 terms. In the same range the only fixed points are 1, 2, and 9, and it is likely no more exist.

Examples

			a(9) = 9 as a(8) = 12 which has six divisors, and 9 is the smallest unused number that shares a factor with 6.
		

Links

• Scott R. Shannon, Image of the first 1000 terms. The green line is y = n.

Crossrefs

Cf. A356431, A356432, A000005, A354960, A348086.