cp's OEIS Frontend

A357315 Numbers m such that for all k < m, at least one of m*k - 1 and m*k + 1 is squarefree.

%I A357315 #65 Jan 04 2023 15:53:02
%S A357315 1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,22,24,30,32,36,42,44,48,50,
%T A357315 52,54,56,62,64,66,70,72,78,84,90,96,126,132,140,144,150,156,168,180,
%U A357315 198,210,216,228,240,246,264,270,360,378,390,414,420,450,510,546,630,780,840,1230,1470,1680,5250
%N A357315 Numbers m such that for all k < m, at least one of m*k - 1 and m*k + 1 is squarefree.
%C A357315 Conjecture: this sequence is finite.
%C A357315 a(70) > 2*10^7, if it exists. - _Giovanni Resta_, Oct 20 2022
%H A357315 Sidney Cadot, <a href="/A357315/b357315.txt">Table of n, a(n) for n = 1..69</a>
%e A357315 11 is not in this sequence because 11*5-1=54, 11*5+1=56 are both squareful numbers and 11*9-1=98, 11*9+1=100 are both squareful numbers.
%t A357315 q[n_] := AllTrue[Range[n - 1]*n, SquareFreeQ[# - 1] || SquareFreeQ[# + 1] &]; Select[Range[2000], q] (* _Amiram Eldar_, Oct 20 2022 *)
%o A357315 (Magma) [n: n in [1..2000] | #[k: k in [1..n-1] | not IsSquarefree(n*k-1) and not IsSquarefree(n*k+1)] eq 0];
%o A357315 (PARI) isok(m) = for (k=1, m-1, if (!issquarefree(m*k - 1) && !issquarefree(m*k + 1), return(0));); return(1); \\ _Michel Marcus_, Oct 20 2022
%Y A357315 Cf. A005117, A013929, A257771, A281192.
%K A357315 nonn
%O A357315 1,2
%A A357315 _Juri-Stepan Gerasimov_, Oct 17 2022
%E A357315 Name edited by _Thomas Scheuerle_, Oct 20 2022
%E A357315 a(69) from _Amiram Eldar_, Oct 20 2022