A330597 Squarefree numbers in which all substrings are squarefree.

1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 21, 22, 23, 26, 31, 33, 35, 37, 51, 53, 55, 57, 61, 62, 65, 66, 67, 71, 73, 77, 111, 113, 115, 131, 133, 137, 151, 155, 157, 173, 177, 211, 213, 215, 217, 221, 222, 223, 226, 231, 233, 235, 237, 262, 265, 266, 267, 311, 313

Offset

1,2

Comments

This sequence is finite, the last term being a(1690) = 77377717.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1690

Rémy Sigrist, PARI program for A330597

Example

1, 3, 7, 13, 37 and 137 are all squarefree, hence 137 is a term.

Mathematica

sfQ[k_]:=With[{i=IntegerDigits[k]}, AllTrue[Flatten[Table[ FromDigits/@ Partition[ i, n, 1], {n, IntegerLength[k]}]], SquareFreeQ]]; Select[ Range[ 350], sfQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 09 2020 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A005117, A085823 (prime variant), A202262 (composite variant).

Sequence in context: A098962 A073485 A062101 * A352336 A283599 A096530

Adjacent sequences: A330594 A330595 A330596 * A330598 A330599 A330600

Keyword

nonn,base,fini,full

Author

Rémy Sigrist, Dec 19 2019

Status

approved