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A008847
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Numbers k such that sum of divisors of k^2 is a square.
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11
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1, 9, 20, 180, 1306, 1910, 11754, 17190, 32486, 38423, 47576, 48202, 50920, 51590, 83884, 104855, 132682, 198534, 247863, 292374, 300876, 312374, 313929, 334330, 345807, 376095, 428184, 433818, 458280, 464310, 469623, 498892, 623615, 754956, 768460, 787127, 943695, 985369
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.
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LINKS
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FORMULA
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MAPLE
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with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;
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MATHEMATICA
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s = {}; Do[ If[IntegerQ[ Sqrt[ DivisorSigma[1, n^2]]], Print[n]; AppendTo[s, n]], {n, 10^6}]; s (* Jean-François Alcover, May 05 2011 *)
Select[Range[1000000], IntegerQ[Sqrt[DivisorSigma[1, #^2]]]&] (* Harvey P. Dale, Aug 22 2011 *)
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PROG
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(Haskell)
a008847 n = a008847_list !! (n-1)
a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..]
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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