A116014 Numbers k such that k + sigma(k) + sigma(sigma(k)) is a square.

2, 9, 19, 98, 141, 176, 319, 396, 467, 691, 729, 970, 1113, 1279, 1447, 1473, 1873, 1974, 2403, 3712, 5208, 5965, 6777, 7183, 8353, 8769, 8881, 8962, 10137, 10180, 10771, 11314, 12016, 12241, 13624, 15196, 19683, 19705, 20053, 20553, 21241

Offset: 1

Author

Giovanni Resta, Feb 13 2006

Keywords

• nonn

Examples

			1113 + sigma(1113) + sigma(sigma(1113)) = 89^2.
		

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A116012, A116013, A116015.

Programs

Mathematica

okQ[n_]:=Module[{dsn=DivisorSigma[1,n]}, IntegerQ[Sqrt[n+dsn+DivisorSigma[1,dsn]]]]; Select[Range[22000],okQ]  (* Harvey P. Dale, Jan 23 2011 *)

PARI

is(n)=my(s=sigma(n)); issquare(n+s+sigma(s)) \\ Charles R Greathouse IV, Jul 30 2016