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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A000203, A007503.

Sequence in context: A017724 A009841 A038650 * A078962 A000508 A191092

Adjacent sequences: A224438 A224439 A224440 * A224442 A224443 A224444

Keyword

nonn

Author

Jayanta Basu, Apr 09 2013

Status

approved