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A083540
Numbers k such that A083539(k) is a square; solutions x to sigma(x+1)*sigma(x)=y^2 for some y.
3
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
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
EXAMPLE
x=30: sigma(30)=72, sigma(31)=32, product = 72*32 = 256*9 = 24^2.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 21 2003
STATUS
approved