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%I #11 May 09 2020 11:11:47
%S 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,
%T 66,67,71,73,77,111,113,115,131,133,137,151,155,157,173,177,211,213,
%U 215,217,221,222,223,226,231,233,235,237,262,265,266,267,311,313
%N Squarefree numbers in which all substrings are squarefree.
%C This sequence is finite, the last term being a(1690) = 77377717.
%H Rémy Sigrist, <a href="/A330597/b330597.txt">Table of n, a(n) for n = 1..1690</a>
%H Rémy Sigrist, <a href="/A330597/a330597.gp.txt">PARI program for A330597</a>
%e 1, 3, 7, 13, 37 and 137 are all squarefree, hence 137 is a term.
%t 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 *)
%o (PARI) See Links section.
%Y Cf. A005117, A085823 (prime variant), A202262 (composite variant).
%K nonn,base,fini,full
%O 1,2
%A _Rémy Sigrist_, Dec 19 2019