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

1,2

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.

Links

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

Example

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.

Crossrefs

Cf. A000120, A032741, A005179, A027751.

Sequence in context: A356511 A162374 A323289 * A357601 A065885 A274331

Adjacent sequences: A355371 A355372 A355373 * A355375 A355376 A355377

Keyword

nonn,base,look

Author

Scott R. Shannon, Jun 30 2022

Status

approved