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%I #40 Nov 03 2023 12:36:36
%S 1,9,20,180,1306,1910,11754,17190,32486,38423,47576,48202,50920,51590,
%T 83884,104855,132682,198534,247863,292374,300876,312374,313929,334330,
%U 345807,376095,428184,433818,458280,464310,469623,498892,623615,754956,768460,787127,943695,985369
%N Numbers k such that sum of divisors of k^2 is a square.
%C These are the square roots of squares in A006532. - _M. F. Hasler_, Oct 23 2010
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
%D I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.
%H Donovan Johnson, <a href="/A008847/b008847.txt">Table of n, a(n) for n = 1..400</a> (first 161 terms from Zak Seidov)
%F A163763(n) = sqrt(sigma(A008847(n)^2)). - _M. F. Hasler_, Oct 16 2010
%F a(n) = sqrt(A008848(n)). - _Zak Seidov_, May 01 2016
%p with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;
%t s = {}; Do[ If[IntegerQ[ Sqrt[ DivisorSigma[1, n^2]]], Print[n]; AppendTo[s, n]], {n, 10^6}]; s (* _Jean-François Alcover_, May 05 2011 *)
%t Select[Range[1000000],IntegerQ[Sqrt[DivisorSigma[1,#^2]]]&] (* _Harvey P. Dale_, Aug 22 2011 *)
%o (PARI) is_A008847(n)=issquare(sigma(n^2)) \\ _M. F. Hasler_, Oct 23 2010
%o (Haskell)
%o a008847 n = a008847_list !! (n-1)
%o a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..]
%o -- _Reinhard Zumkeller_, Mar 27 2013
%Y Cf. A008848, A008849, A008850, A163763.
%Y Cf. A000203, A010052, A000290.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_
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