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 A075769 A Wallis pair (x,y) satisfies sigma(x^2) = sigma(y^2); sequence gives y's for indecomposable Wallis pairs with x < y (ordered by values of x). 5
 5, 407, 489, 749, 878, 1451, 1102, 1208, 1943, 1528, 1809, 1605, 2557, 3097, 3730, 4829, 6061, 4880, 6341, 6172, 7715, 7067, 10071, 17441, 11020, 17531, 14397, 17441, 14001, 24161, 24613, 14288, 14795, 20396, 25495, 22577, 19784, 15836, 19795, 27713, 30959 (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, 2]] (* Jean-François Alcover, Sep 26 2013 *) CROSSREFS Cf. A075768, A072182, A072186, A077053. Sequence in context: A198535 A128866 A221047 * A046274 A221700 A216089 Adjacent sequences:  A075766 A075767 A075768 * A075770 A075771 A075772 KEYWORD nonn,nice AUTHOR N. J. A. Sloane, Oct 13 2002 EXTENSIONS Corrected and extended by Klaus Brockhaus, Oct 22 2002 19795 from Jean-François Alcover, Dec 28 2012 Offset corrected by Donovan Johnson, Sep 18 2013 STATUS approved

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)