A221856 Square numbers n for which sigma(n) + d(n) is also a perfect square.

9, 16, 36, 278784, 251381025, 2390623236, 240055902025, 354328515025, 1022960302225, 1298266542225, 6824670333649, 9433221536025, 16614933604164, 33314541015625, 474897452948164, 500279020818724, 1387202986290276, 2162188899431649, 16053088159411524

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

16 is in the list since 16 = 4^2 and sigma(16)+d(16) = 36 = 6^2. Also 278784 = 528^2 and sigma(278784)+d(278784) = 883600 = 940^2.

Mathematica

Sqd[n_] := Sqrt[DivisorSigma[1, n] + DivisorSigma[0, n]]; t = {}; Do[If[IntegerQ[Sqd[n^2]], AppendTo[t, n^2]], {n, 1500000}]; t

Crossrefs

Cf. A007503.

Sequence in context: A076621 A134937 A076431 * A309273 A358627 A282470

Adjacent sequences: A221853 A221854 A221855 * A221857 A221858 A221859

Keyword

nonn

Author

Jayanta Basu, Apr 10 2013

Extensions

a(11)-a(19) from Donovan Johnson, Apr 10 2013

Status

approved