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).

5, 15, 35, 45, 55, 65, 85, 95, 105, 115, 135, 145, 155, 165, 185, 195, 205, 215, 235, 245, 255, 265, 285, 295, 305, 315, 335, 345, 355, 365, 385, 395, 405, 407, 415, 435, 445, 455, 465, 485, 495, 505, 489, 515, 535, 545, 555, 565, 585, 595, 605, 615, 635

Offset: 1

Author

N. J. A. Sloane, Oct 19 2002

Keywords

• nonn
• easy

Comments

5*A045572 is included in this sequence. - Benoit Cloitre, Oct 22 2002

Examples

			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), ...
		

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..10000

Crossrefs

Cf. A072182, A075768, A075769.

Programs

Haskell

a072186 n = a072186_list !! (n-1)
-- a072186_list defined in A072182.  -- Reinhard Zumkeller, Sep 18 2013

Mathematica

w = {}; m = 550;
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}];
w[[All, 2]] (* Jean-François Alcover, Oct 01 2019 *)

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],","))}

Extensions

Extended by Klaus Brockhaus and Benoit Cloitre, Oct 22 2002