A083540 Numbers k such that A083539(k) is a square; solutions x to sigma(x+1)*sigma(x)=y^2 for some y.

14, 30, 51, 161, 186, 206, 223, 329, 552, 713, 759, 869, 957, 994, 995, 1248, 1334, 1364, 1634, 1715, 1819, 2093, 2133, 2584, 2685, 2820, 2821, 2974, 3115, 3145, 3485, 4212, 4308, 4312, 4364, 4408, 4649

Offset: 1

Author

Labos Elemer, May 21 2003

Keywords

• nonn

Examples

			x=30: sigma(30)=72, sigma(31)=32, product = 72*32 = 256*9 = 24^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000203, A083539, A060780, A060781, A083538.

Programs

Mathematica

Do[s=Sqrt[DivisorSigma[1, n+1]*DivisorSigma[1, n]]; If[IntegerQ[s], Print[n]], {n, 1, 5000}]
Flatten[Position[Times@@@Partition[DivisorSigma[1,Range[5000]],2,1], ?(IntegerQ[Sqrt[#]]&)]] (* _Harvey P. Dale, Mar 07 2016 *)