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A322688
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Two-column table read by rows: Primitive distinct pairs that have the same value of phi, sigma, and tau.
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11
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568, 638, 1824, 1836, 3051, 3219, 4185, 4389, 4960, 5236, 6368, 6764, 7749, 8151, 9184, 9724, 9760, 11050, 11032, 12470, 11176, 12586, 13420, 14350, 15169, 15265, 17376, 19206, 18788, 20150, 23848, 26866, 26355, 27962, 26784, 29260, 28809, 30381, 30199, 30217, 32128, 33128, 32940, 37050, 34144, 36244, 37592, 39795
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OFFSET
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1,1
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COMMENTS
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The terms are consecutive pairs, ordered so that (A) a(2i-1) < a(2i) for i > 0, and (B) a(2i+1) < a(2i+3) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive pair, then multiplying the terms in that pair by k gives another solution - see A134922. In Burton's book (see references), problem 3 in section 7.2 asks the reader to prove a special case for (568,638).
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REFERENCES
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David Burton, Elementary Number Theory, 4th edition, 1998, section 7.2.
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LINKS
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EXAMPLE
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phi(568)=phi(638)=280; sigma(568)=sigma(638)=1080; tau(568)=tau(638)=8.
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CROSSREFS
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Cf. A134922, A322687, A322689, A322690, A322691, A322692, A322693, A322694, A322695, A322696, A322696.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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