A152219 Numbers k such that k! - 1 is divisible by a square greater than one.

9, 15, 105, 112, 609, 4929

Offset: 1

Author

Artur Jasinski, Nov 29 2008

Keywords

• nonn
• more

Comments

Primes p such that p^2 divides m!-1 for some integer m

A152220.

Crossrefs

Cf. A064237.

Programs

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