A072182 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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, 1]] (* 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][1], ", "))}

(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

CROSSREFS

Cf. A072186, A075768, A075769.

Cf. A000203, A000290.

Sequence in context: A207408 A366998 A064444 * A009906 A357719 A194432

Adjacent sequences: A072179 A072180 A072181 * A072183 A072184 A072185