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 A075768 A Wallis pair (x,y) satisfies sigma(x^2) = sigma(y^2); sequence gives x's for indecomposable Wallis pairs with x < y (ordered by values of x). 5
 4, 326, 406, 627, 740, 880, 888, 1026, 1110, 1284, 1510, 1528, 2013, 2072, 3216, 3260, 3912, 4866, 4946, 5064, 5064, 5829, 7248, 9768, 10536, 10686, 11836, 12122, 13066, 13398, 13986, 14248, 14397, 15000, 15000, 15430, 15504, 15544, 15544, 18582, 18678 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If (x,y) and (u,v) are Wallis pairs, a is from (x,y) and c is from (u,v) and gcd(a,c)=1, b is from (x,y) and d is from(u,v) and gcd(b,d)=1, then (ac,bd) is also a Wallis pair. Such pairs are called decomposable. If (x,y) and (cx,cy) are Wallis pairs then (cx,cy) is also called decomposable. REFERENCES I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002. LINKS Donovan Johnson, Table of n, a(n) for n = 1..1000 EXAMPLE (4,5) is a Wallis pair since sigma(16) = sigma(25) = 31. MATHEMATICA xmax = 20000; sigma[n_] := sigma[n] = DivisorSigma[1, n]; WallisQ[{x_, y_}] := sigma[x^2] == sigma[y^2]; pairs = Reap[Do[Do[ If[WallisQ[{x, y}] && ! (GCD[x, y] != 1 && WallisQ[{x, y}/GCD[x, y]]), Print[{x, y}, " is a Wallis pair to be tested for indecomposability"]; Sow[{x, y}]], {y, x + 1, 2.2*x}], {x, 1, xmax}]][[2, 1]]; indecomposableQ[{x0_, y0_}] := (pf = pairs // Flatten; sx = Intersection[Most@Divisors[x0], pf]; sy = Intersection[Most@Divisors[y0], pf]; xy = Outer[List, sx, sy] // Flatten[#, 1] &; sel = Select[xy, WallisQ[#] && WallisQ[{x0, y0}/#] &]; sel == {}); Select[pairs, indecomposableQ][[All, 1]] (* Jean-François Alcover, Sep 26 2013 *) CROSSREFS Cf. A075769, A072182, A072186, A077053. Sequence in context: A053917 A005832 A195501 * A135442 A086895 A293241 Adjacent sequences:  A075765 A075766 A075767 * A075769 A075770 A075771 KEYWORD nonn,nice AUTHOR N. J. A. Sloane, Oct 13 2002 EXTENSIONS Corrected and extended by Klaus Brockhaus, Oct 22 2002 Offset corrected by Donovan Johnson, Sep 18 2013 STATUS approved

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Last modified September 21 19:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)