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 A008848 Squares whose sum of divisors is a square. 8
 1, 81, 400, 32400, 1705636, 3648100, 138156516, 295496100, 1055340196, 1476326929, 2263475776, 2323432804, 2592846400, 2661528100, 7036525456, 10994571025, 17604513124, 39415749156, 61436066769, 85482555876, 90526367376, 97577515876, 98551417041 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Solutions to sigma(x^2) = (2k+1)^2. - Labos Elemer, Aug 22 2002 Intersection of A006532 and A000290. The product of any two coprime terms is also in this sequence. - Charles R Greathouse IV, May 10 2011 Also intersection of A069070 and A000290. - Michel Marcus, Oct 06 2013 REFERENCES 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. LINKS Donovan Johnson, Table of n, a(n) for n = 1..400 EXAMPLE n=32400: sigma[32400] = 116281 = 341^2 = 121*961. MATHEMATICA Do[s=DivisorSigma[1, n^2]; If[IntegerQ[Sqrt[s]]&&Mod[s, 2]==1, Print[n^2]], {n, 1, 10000000}] (* Labos Elemer *) Select[Range[320000]^2, IntegerQ[Sqrt[DivisorSigma[1, #]]]&] (* Harvey P. Dale, Feb 22 2015 *) PROG (PARI) for(n=1, 1e6, if(issquare(sigma(n^2)), print1(n^2", "))) \\ Charles R Greathouse IV, May 10 2011 CROSSREFS a(n) = A008847(n)^2. Cf. A028982, A001248, A000203. Sequence in context: A017498 A097025 A074387 * A237182 A237176 A102741 Adjacent sequences:  A008845 A008846 A008847 * A008849 A008850 A008851 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)