0,2

Finite idempotent functions are identity maps on finite subsets, counting the empty function as the idempotent on the empty set.

Writing (prime(i))^j as i:j, we have the following table of examples:

Primal Codes of Finite Idempotent Functions on Positive Integers

` ` ` 1 = { }

` ` ` 2 = 1:1

` ` ` 9 = ` ` 2:2

` ` `18 = 1:1 2:2

` ` 125 = ` ` ` ` 3:3

` ` 250 = 1:1 ` ` 3:3

` `1125 = ` ` 2:2 3:3

` `2250 = 1:1 2:2 3:3

` `2401 = ` ` ` ` ` ` 4:4

` `4802 = 1:1 ` ` ` ` 4:4

` 21609 = ` ` 2:2 ` ` 4:4

` 43218 = 1:1 2:2 ` ` 4:4

`300125 = ` ` ` ` 3:3 4:4

`600250 = 1:1 ` ` 3:3 4:4

2701125 = ` ` 2:2 3:3 4:4

5402250 = 1:1 2:2 3:3 4:4

Cf. A076954, A106177, A108352, A108371, A109301.

Sequence in context: A083423 A068978 A006226 this_sequence A075537 A075340 A031316

Adjacent sequences: A109295 A109296 A109297 this_sequence A109299 A109300 A109301

nonn

Jon Awbrey (jawbrey(AT)att.net), Jul 06 2005