login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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-Fran├žois 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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)