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A008847 Numbers k such that sum of divisors of k^2 is a square. 11

%I

%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 Zak Seidov and 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-Fran├žois 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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Last modified June 19 12:57 EDT 2021. Contains 345129 sequences. (Running on oeis4.)