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 A008847 Numbers k such that sum of divisors of k^2 is a square. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are the square roots of squares in A006532. - M. F. Hasler, Oct 23 2010 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 Zak Seidov and Donovan Johnson, Table of n, a(n) for n = 1..400 (first 161 terms from Zak Seidov) FORMULA A163763(n) = sqrt(sigma(A008847(n)^2)). - M. F. Hasler, Oct 16 2010 a(n)=sqrt(A008848(n)). - Zak Seidov, May 01 2016 MAPLE with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od; MATHEMATICA 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 *) PROG (PARI) is_A008847(n)=issquare(sigma(n^2)) \\ M. F. Hasler, Oct 23 2010 (Haskell) a008847 n = a008847_list !! (n-1) a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..] -- Reinhard Zumkeller, Mar 27 2013 CROSSREFS Cf. A008848, A008849, A008850, A163763. Cf. A000203, A010052, A000290. Sequence in context: A321723 A282763 A013338 * A143243 A157812 A218164 Adjacent sequences:  A008844 A008845 A008846 * A008848 A008849 A008850 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified May 12 06:44 EDT 2021. Contains 343820 sequences. (Running on oeis4.)