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A072186 A Wallis pair (x,y) satisfies sigma(x^2) = sigma(y^2); sequence gives y's for Wallis pairs with x < y (ordered by values of x).

%I A072186 #22 Oct 01 2019 09:13:04
%S A072186 5,15,35,45,55,65,85,95,105,115,135,145,155,165,185,195,205,215,235,
%T A072186 245,255,265,285,295,305,315,335,345,355,365,385,395,405,407,415,435,
%U A072186 445,455,465,485,495,505,489,515,535,545,555,565,585,595,605,615,635
%N A072186 A Wallis pair (x,y) satisfies sigma(x^2) = sigma(y^2); sequence gives y's for Wallis pairs with x < y (ordered by values of x).
%C A072186 5*A045572 is included in this sequence. - _Benoit Cloitre_, Oct 22 2002
%D A072186 I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.
%H A072186 Donovan Johnson, <a href="/A072186/b072186.txt">Table of n, a(n) for n = 1..10000</a>
%e A072186 The first few pairs are all multiples of the first pair (4,5): (4, 5), (12, 15), (28, 35), (36, 45), (44, 55), (52, 65), ...
%t A072186 w = {}; m = 550;
%t A072186 Do[q = DivisorSigma[1, x^2]; sq = Sqrt[q] // Floor; Do[If[q == DivisorSigma[1, y^2], AppendTo[w, {x, y}]], {y, x + 1, sq}], {x, 1, m}];
%t A072186 w[[All, 2]] (* _Jean-François Alcover_, Oct 01 2019 *)
%o A072186 (PARI) {w=[]; m=550; for(x=1,m,q=sigma(x^2); sq=sqrtint(q); for(y=x+1,sq,if(q==sigma(y^2), w=concat(w,[[x,y]])))); for(j=1,matsize(w)[2],print1(w[j][2],","))}
%o A072186 (Haskell)
%o A072186 a072186 n = a072186_list !! (n-1)
%o A072186 -- a072186_list defined in A072182.  -- _Reinhard Zumkeller_, Sep 18 2013
%Y A072186 Cf. A072182, A075768, A075769.
%K A072186 nonn,easy
%O A072186 1,1
%A A072186 _N. J. A. Sloane_, Oct 19 2002
%E A072186 Extended by _Klaus Brockhaus_ and _Benoit Cloitre_, Oct 22 2002