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

1,1

Comments

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

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

Example

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), ...

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 *)

Prog

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

Crossrefs

Cf. A072182, A075768, A075769.

Sequence in context: A346752 A292955 A295005 * A051807 A034052 A233348

Adjacent sequences: A072183 A072184 A072185 * A072187 A072188 A072189

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 19 2002

Extensions

Extended by Klaus Brockhaus and Benoit Cloitre, Oct 22 2002

Status

approved