OFFSET
1,1
COMMENTS
All terms are multiples of 4. Whether n is congruent to 1 or 3 mod 4, n^2 is congruent to 1 mod 3 and therefore mu(n^2 - 1) = 0. - Alonso del Arte, Dec 12 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
36 is in this sequence because 35 and 37 are both squarefree.
64 is not in this sequence because 63 = 3^2 * 7.
MATHEMATICA
Select[Table[n^2, {n, 150}], SquareFreeQ[# - 1] && SquareFreeQ[# + 1] &] (* Vaclav Kotesovec, Dec 11 2013 *)
Select[Range[150]^2, Abs[MoebiusMu[# - 1] MoebiusMu[# + 1]] == 1 &] (* Alonso del Arte, Dec 11 2013 *)
SequencePosition[Table[Which[IntegerQ[Sqrt[n]], 1, SquareFreeQ[n], 2, True, 0], {n, 25000}], {2, 1, 2}][[;; , 1]]+1 (* Harvey P. Dale, Jun 27 2023 *)
PROG
(PARI) forstep(n=2, 1e3, [2, 2, 6, 2, 2, 2, 2], if(issquarefree(n-1) && issquarefree(n+1) && issquarefree(n^2+1), print1(n^2", "))) \\ Charles R Greathouse IV, Mar 18 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Irina Gerasimova, Dec 09 2013
STATUS
approved