A338219 Lexicographically earliest divisibility sequence consisting only of distinct squarefree numbers.

1, 2, 3, 6, 5, 30, 7, 42, 15, 10, 11, 210, 13, 14, 105, 462, 17, 330, 19, 390, 21, 22, 23, 2310, 35, 26, 165, 546, 29, 2730, 31, 6006, 33, 34, 70, 30030, 37, 38, 39, 46410, 41, 3570, 43, 66, 1155, 46, 47, 39270, 77, 770, 51, 78, 53, 4290, 55, 9282, 57, 58, 59

Offset

1,2

Comments

This sequence is a permutation of the squarefree numbers (A005117).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A001221(a(n)))

Rémy Sigrist, PARI program for A338219

Index to divisibility sequences

Formula

a(p) = p for any prime number p.

a(p) < a(n) for any prime number p and n > p.

Example

For n = 1:
- we choose a(1) = 1.
For n = 2:
- a(2) must be divisible by a(1) = 1,
- we choose a(2) = 2.
For n = 3:
- a(3) must be divisible by a(1) = 1,
- we choose a(3) = 3.
For n = 4:
- a(4) must be divisible by a(1) = 1 and a(2) = 2,
- we choose a(4) = 6.
For n = 5:
- a(5) must be divisible by a(1) = 1,
- we choose a(5) = 5.
For n = 6:
- a(6) must be divisible by a(1) = 1, a(2) = 2 and a(3) = 3,
- we choose a(6) = 30.

Prog

(PARI) See Links section.

Crossrefs

See A338461 for a similar sequence.

Cf. A001221, A005117.

Sequence in context: A206242 A327454 A124655 * A066838 A228151 A276087

Adjacent sequences: A338216 A338217 A338218 * A338220 A338221 A338222

Keyword

nonn,look

Author

Rémy Sigrist, Jan 30 2021

Status

approved