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

Author

Rémy Sigrist, Dec 19 2019

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..1690
• Rémy Sigrist, PARI program for A330597

Crossrefs

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

Programs

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 *)

PARI

See Links section.