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Numbers n such that sigma(n) * antisigma(n) is a perfect square, where antisigma(n) = sum of the non-divisors of n that are between 1 and n.
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%I #7 Feb 11 2014 19:05:31

%S 1,2,15,20,24,28,104,224,5065,766192670

%N Numbers n such that sigma(n) * antisigma(n) is a perfect square, where antisigma(n) = sum of the non-divisors of n that are between 1 and n.

%e sigma(15) * antisigma(15) = 24 * 96 = 48^2, so 15 is a term of the sequence.

%t l = {}; Do[s = DivisorSigma[1, n]; a = (n (n + 1)/2) - s; If[IntegerQ[Sqrt[a*s]], l = Append[l, n]], {n, 1, 10^5}]; l

%K nonn

%O 1,2

%A _Joseph L. Pe_, Oct 23 2002

%E a(10) from _Donovan Johnson_, Jan 18 2012