A355483 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of 1-bits in the binary expansion of a(n) equals the number of divisors of a(n-1).

1, 2, 3, 5, 6, 15, 23, 9, 7, 10, 27, 29, 12, 63, 95, 30, 255, 383, 17, 18, 111, 39, 43, 20, 119, 45, 123, 46, 51, 53, 24, 447, 54, 479, 33, 57, 58, 60, 4095, 16777215, 79228162514264337593543950335

Offset: 1

Author

Scott R. Shannon, Jul 03 2022

Keywords

• nonn
• base

Comments

This sequence is similar to A355482 except that here all divisors of a(n-1) are counted.

The fixed points in the first 41 terms are 1,2,3,10.

It is unknown if all numbers eventually appear.

Since a(41) has 6144 divisors, a(42) = 2^6144 - 1 is a 1850-digit number.

Examples

			a(7) = 23 = 10111_2 as a(6) = 15 which has four divisors, and 23 is the smallest unused number that has four 1-bits in its binary expansion.
		

Crossrefs

Cf. A355482 (proper divisors), A355374, A000120, A032741, A005179, A027751.