A072182 - OEIS

%I #23 Oct 01 2019 09:13:13

%S 4,12,28,36,44,52,68,76,84,92,108,116,124,132,148,156,164,172,188,196,

%T 204,212,228,236,244,252,268,276,284,292,308,316,324,326,332,348,356,

%U 364,372,388,396,404,406,412,428,436,444,452,468,476,484,492,508,516

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

%C 4*A045572 is included in this sequence. - _Benoit Cloitre_, Oct 22 2002

%C D. Johnson remarks that some terms are repeated, e.g., a(139)=a(140)=1284 forms a Wallis pair with A072186(139)=1528 and also with A072186(140)=1605. - _M. F. Hasler_, Sep 15 2013

%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="/A072182/b072182.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 w = {}; m = 550;

%t 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 w[[All, 1]] (* _Jean-François Alcover_, Oct 01 2019 *)

%o (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][1],","))}

%o (Haskell)

%o a072182 n = a072182_list !! (n-1)

%o (a072182_list, a072186_list) = unzip wallisPairs

%o   wallisPairs = [(x, y) | (y, sy) <- tail ws,

%o                           (x, sx) <- takeWhile ((< y) . fst) ws, sx == sy]

%o                 where ws = zip [1..] $ map a000203 $ tail a000290_list

%o -- _Reinhard Zumkeller_, Sep 17 2013

%Y Cf. A072186, A075768, A075769.

%Y Cf. A000203, A000290.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Oct 19 2002

%E Extended by _Klaus Brockhaus_ and _Benoit Cloitre_, Oct 22 2002