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A330597 Squarefree numbers in which all substrings are squarefree. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A283599 A096530 A299157

Adjacent sequences:  A330594 A330595 A330596 * A330598 A330599 A330600

KEYWORD

nonn,base,fini,full

AUTHOR

Rémy Sigrist, Dec 19 2019

STATUS

approved

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Last modified September 23 03:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)