A355482 a(1) = 2; 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 proper divisors of a(n-1).

2, 4, 3, 8, 7, 16, 15, 11, 32, 31, 64, 63, 47, 128, 127, 256, 255, 191, 512, 511, 13, 1024, 1023, 223, 2048, 2047, 14, 19, 4096, 4095, 8388607, 21, 22, 25, 5, 8192, 8191, 16384, 16383, 239, 32768, 32767, 247, 26, 28, 55, 35, 37, 65536, 65535, 49151, 38, 41, 131072, 131071, 262144, 262143

Offset: 1

Author

Scott R. Shannon, Jul 03 2022

Keywords

• nonn
• base

Comments

This sequence is similar to A355374 but the rules for determining a(n) are reversed. The only fixed point in the first 145 terms is a(3) = 3. It is unknown if all numbers eventually appear. The last known term is a(145) which is a 154 digit number whose complete factorization is unknown.

Examples

			a(7) = 15 = 1111_2 as a(6) = 16 which has four proper divisors, and 15 is the smallest unused number that has four 1-bits in its binary expansion.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..145

Crossrefs

Cf. A355483 (all divisors), A355374, A000120, A032741, A005179, A027751.