

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).


5



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
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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]] (* JeanFrançois 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 !! (n1)
(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: A212522 A207408 A064444 * A009906 A194432 A220512
Adjacent sequences: A072179 A072180 A072181 * A072183 A072184 A072185


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 19 2002


EXTENSIONS

Extended by Klaus Brockhaus and Benoit Cloitre, Oct 22 2002


STATUS

approved



