A355374 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of proper divisors of a(n) equals the number of 1-bits in the binary expansion of a(n-1).

1, 2, 3, 4, 5, 9, 25, 6, 49, 8, 7, 10, 121, 12, 169, 16, 11, 14, 15, 81, 21, 22, 26, 27, 625, 18, 289, 33, 361, 20, 529, 34, 841, 28, 35, 38, 39, 2401, 32, 13, 46, 14641, 24, 961, 44, 51, 28561, 48, 1369, 64, 17, 1681, 45, 83521, 729, 15625, 30, 130321, 1024, 19, 55, 50, 57, 279841, 117649

Offset: 1

Author

Scott R. Shannon, Jun 30 2022

Keywords

• nonn
• base
• look

Comments

In the first 700 terms the fixed points are 1, 2, 3, 4, 5, 16, 21, 22, 35, 48, 168, 412, 428. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(7) = 25 as a(6) = 9 = 1001_2 which has two 1-bits in its binary expansion, and 25 is the smallest unused number that has two proper divisors.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..713

Crossrefs

Cf. A000120, A032741, A005179, A027751.