A152219 Numbers k such that k! - 1 is divisible by a square greater than one.
9, 15, 105, 112, 609, 4929
Offset: 1
Crossrefs
Cf. A064237.
Programs
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Mathematica
aa = {}; Do[If[(Sqrt[n! - 1] /. Sqrt[_] -> 1) > 1, Print[n]; AppendTo[aa, n]], {n, 1, 1000}]; aa (* alternate program *) nfdsQ[n_]:=AnyTrue[Rest[Divisors[n!-1]],IntegerQ[Sqrt[#]]&]; Select[Range[ 2,610],nfdsQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 24 2020 *)
Extensions
a(6) from Artur Jasinski, Nov 30 2008
Definition clarified by Harvey P. Dale, May 24 2020
Comments
A152220.