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Search: id:A075769
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| A075769 |
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A Wallis pair (x,y) satisfies sigma(x^2) = sigma(y^2); sequence gives y's for indecomposable Wallis pairs with x < y (ordered by values of x). |
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5
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| 5, 407, 489, 749, 878, 1451, 1102, 1208, 1943, 1528, 1809, 1605, 2557, 3097, 3730, 4829, 6061, 4880, 6341, 6172, 7715, 7067, 10071, 17441, 11020, 17531, 14397, 17441, 14001, 24161, 24613, 14288, 14795, 20396, 25495, 22577, 19784, 15836
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OFFSET
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0,1
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COMMENT
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If (x,y) and (u,v) are Wallis pairs, a is from (x,y) and c is from (u,v) and gcd(a,c)=1, b is from (x,y) and d is from(u,v) and gcd(b,d)=1, then (ac,bd) is also a Wallis pair. Such pairs are called decomposable. If (x,y) and (cx,cy) are Wallis pairs then (cx,cy) is also called decomposable.
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REFERENCES
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I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.
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EXAMPLE
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(4,5) is a Wallis pair since sigma(16) = sigma(25) = 31.
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CROSSREFS
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Cf. A075768, A072182, A072186, A077053.
Sequence in context: A006700 A079011 A128866 this_sequence A046274 A147684 A038003
Adjacent sequences: A075766 A075767 A075768 this_sequence A075770 A075771 A075772
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 13 2002
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EXTENSIONS
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Corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 22 2002
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