OFFSET
1,2
COMMENTS
Conjecture: this sequence is finite.
a(70) > 2*10^7, if it exists. - Giovanni Resta, Oct 20 2022
LINKS
Sidney Cadot, Table of n, a(n) for n = 1..69
EXAMPLE
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.
MATHEMATICA
q[n_] := AllTrue[Range[n - 1]*n, SquareFreeQ[# - 1] || SquareFreeQ[# + 1] &]; Select[Range[2000], q] (* Amiram Eldar, Oct 20 2022 *)
PROG
(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];
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Oct 17 2022
EXTENSIONS
Name edited by Thomas Scheuerle, Oct 20 2022
a(69) from Amiram Eldar, Oct 20 2022
STATUS
approved