A072182 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).

4, 12, 28, 36, 44, 52, 68, 76, 84, 92, 108, 116, 124, 132, 148, 156, 164, 172, 188, 196, 204, 212, 228, 236, 244, 252, 268, 276, 284, 292, 308, 316, 324, 326, 332, 348, 356, 364, 372, 388, 396, 404, 406, 412, 428, 436, 444, 452, 468, 476, 484, 492, 508, 516

Offset: 1

Author

N. J. A. Sloane, Oct 19 2002

Keywords

• nonn
• easy

Comments

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

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

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. A072186, A075768, A075769.

Cf. A000203, A000290.

Programs

Haskell

a072182 n = a072182_list !! (n-1)
(a072182_list, a072186_list) = unzip wallisPairs
  wallisPairs = [(x, y) | (y, sy) <- tail ws,
                          (x, sx) <- takeWhile ((< y) . fst) ws, sx == sy]
                where ws = zip [1..] $ map a000203 $ tail a000290_list
-- Reinhard Zumkeller, Sep 17 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, 1]] (* 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][1],","))}

Extensions

Extended by Klaus Brockhaus and Benoit Cloitre, Oct 22 2002