A130763 Natural numbers such that d(n)!+ 1 is a square, where d(n) is the number of divisors of n, A000005.

6, 8, 10, 14, 15, 16, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187

Offset: 1

Author

Giovanni Teofilatto, Aug 17 2007

Keywords

• nonn

Comments

It is generally assumed that the Diophantine equation n! + 1 = m^2 can only be solved for n = 4,5,7. - Stefan Steinerberger, Aug 21 2007

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005.

Programs

Mathematica

Select[Range[1000], IntegerQ[Sqrt[Length[Divisors[ # ]]! + 1]] &] (* Stefan Steinerberger, Aug 21 2007 *)
Select[Range[200],IntegerQ[Sqrt[DivisorSigma[0,#]!+1]]&] (* Harvey P. Dale, Aug 04 2022 *)

Extensions

More terms from Stefan Steinerberger, Aug 21 2007