A224441 Numbers n such that sigma(n)+d(n) and sigma(n+1)+d(n+1) are perfect squares.

61, 2369, 4469, 8460, 13208, 44790, 162734, 281560, 283938, 334469, 500465, 533045, 609953, 871853, 962247, 1317885, 1741445, 1792745, 2499845, 3013246, 4099031, 5646629, 7009389, 7012135, 8396781, 8740480, 8822093, 11146381, 11957693, 15002679, 18895694

Offset: 1

Author

Jayanta Basu, Apr 09 2013

Keywords

• nonn

Examples

			61 is in the list since sigma(61)+d(61)=64 and sigma(62)+d(62)=100.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000005, A000203, A007503.

Programs

Mathematica

Sqd[n_] := Sqrt[DivisorSigma[1, n] + DivisorSigma[0, n]]; t = {}; Do[If[IntegerQ[Sqd[n]] && IntegerQ[Sqd[n + 1]], AppendTo[t, n]], {n, 20000000}]; t
SequencePosition[Table[If[IntegerQ[Sqrt[DivisorSigma[0,n]+DivisorSigma[1,n]]],1,0],{n,189*10^5}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2020 *)

PARI

is(n)=issquare(sigma(n)+numdiv(n))&&issquare(sigma(n+1)+ numdiv(n+1)) \\ Charles R Greathouse IV, Apr 09 2013